Term
*Postulate
**Theorem
***Key Concept
****Corollary |
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Definition
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Term
|
Definition
| has the opposite meaning as well as an opposite truth value |
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Term
| Conjunction of a Statement |
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Definition
| compound statement found by joining two or more statements with the word 'and' (^) |
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Term
|
Definition
| educated guess based on known information |
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Term
|
Definition
| reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction |
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Term
|
Definition
| a compound statement formed by joining two or more statements with the word 'or' |
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Term
|
Definition
| statement written in "if-then form" |
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Term
|
Definition
| formed by exchanging the hypothesis and conclusion of the conditional |
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Term
|
Definition
| formed by negating both the hypothesis and the conclusion of the conditional |
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Term
|
Definition
| formed by negating both the hypothesis and conclusion of the converse statement |
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Term
|
Definition
| statements with the same truth values |
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Term
|
Definition
| conjunction of a conditional and its converse |
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Term
|
Definition
| uses facts, rules, definitions, or properties to reach logical conclusions |
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Term
|
Definition
| a form of deductive reasoning that is used to draw conclusions from true conditional statements |
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Term
|
Definition
| If p→q and q→r are true conditionals, then p→r is also true |
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Term
| *Through any two points, there is exactly one line. |
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Definition
|
|
Term
| *Through any three points not on the same line, there is exactly one plane. |
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Definition
|
|
Term
| *A line contains at least two points. |
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Definition
|
|
Term
| *A plane contains at least three points not on the same line. |
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Definition
|
|
Term
| *If two points lie on a plane, then the entire line containing those points lies in that plane. |
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Definition
|
|
Term
| If two lines intersect, then their intersection is exactly one point. |
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Definition
|
|
Term
| If two planes intersect, then their intersection is a line. |
|
Definition
|
|
Term
|
Definition
If M is the midpoint of AB, then AM ≅MB. |
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|
Term
| Segment Addition Postulate |
|
Definition
| If B is between A and C, then AB+BC=AC. |
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Term
|
Definition
| Given [image] and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of [image], such that the measure of the angle formed is r. |
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Term
|
Definition
If R is in the interior of ∠PQS, then m∠PQR + m∠RQS = m∠PQS.
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Term
|
Definition
| If two angles form a linear pair, then they are supplementary angles. |
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Term
|
Definition
| If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles. |
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Term
| **Angles supplementary to the same angle or to congruent angles are congruent. |
|
Definition
|
|
Term
| **Angles complementary to the same angle or to congruent angles are congruent. |
|
Definition
|
|
Term
|
Definition
| If two angles are vertcal angles, then they are congruent. |
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|
Term
| **Perpendicular lines intersect to form four right angles. |
|
Definition
|
|
Term
| **All right angles are congruent. |
|
Definition
|
|
Term
| **Perpendicular lines form congruent adjacent angles. |
|
Definition
|
|
Term
| **If two angles are congruent and suplementary, then each angles is a right angle. |
|
Definition
|
|
Term
| **If two congruent angles form a linear pair, then they are right angles. |
|
Definition
|
|
Term
|
Definition
| lines that do not intersect and are not coplaner |
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|
Term
|
Definition
| a line that intersects two or more lines in a plane at different points |
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|
Term
| Corresponding Angle Postulate |
|
Definition
| If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. |
|
|
Term
| Alternate Interior Angles Theorem |
|
Definition
| If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. |
|
|
Term
| Consecutive Interior Angles Theorem |
|
Definition
| If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. |
|
|
Term
| Alternate Exterior Angles Theorem |
|
Definition
| If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. |
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Term
| Perpendicular Transversal Theorem |
|
Definition
| In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. |
|
|
Term
| *Two nonvertical lines have the same slope if and only if they are parallel. |
|
Definition
|
|
Term
| *Two nonvertical lines are perpendicular if and only if the product of their slopes is -1. |
|
Definition
|
|
Term
| *If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. |
|
Definition
|
|
Term
| ***The distance between two parallel lines is the distance between one of the lines and any point on the other line. |
|
Definition
|
|
Term
| **In a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other. |
|
Definition
|
|
Term
|
Definition
| The sum of the measures of the angles of a triangle is 180. |
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Term
|
Definition
| formed by one side of a triangle and the extension of another. |
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Term
|
Definition
| the interior angles of the triangle not adjacent to a given exterior angle |
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Term
|
Definition
| The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. |
|
|
Term
| ****The acute angles of a right triangle are complementary. |
|
Definition
|
|
Term
| ****There can be at most one right or obtuse angle in a triangle. |
|
Definition
|
|
Term
| Definition of Congruent Triangles (CPCTC) |
|
Definition
| Two triangles are congruent if and only if their corresponding parts are congruent. |
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|
Term
| *Side-Side-Side(SSS) Congruence |
|
Definition
| If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. |
|
|
Term
| *Side-Angle-Side(SAS) Congruence |
|
Definition
| If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. |
|
|
Term
| *Angle-Side-Angle(ASA) Congruence |
|
Definition
| If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. |
|
|
Term
| **Angle-Angle-Side(AAS) Congruence |
|
Definition
| If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent. |
|
|
Term
|
Definition
| If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. |
|
|
Term
| **Hypotenuse-Angle(HA) Congruence |
|
Definition
| If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding angle of another right triangle, then the two triangles are congruent. |
|
|
Term
| **Leg-Angle(LA) Congruence |
|
Definition
| If one leg and an acute angle of one right triangle are congruent to the corresponding leg and angle of another triangle, then the triangles are congruent. |
|
|
Term
| *Hypotenuse-Leg(HL) Congruence |
|
Definition
| If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another triangle, then the triangles are congruent. |
|
|
Term
| Isosceles Triangle Theorem |
|
Definition
| If two sides of a triangle are congruent, then the angles opposite those sides are congruent. |
|
|
Term
| **If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
|
Definition
|
|
Term
| ****A triangle is equliateral if and only if it is equiangluar. |
|
Definition
|
|
Term
| ****Each angle of an equilateal triangle measures 60° |
|
Definition
|
|
Term
| **Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. |
|
Definition
|
|
Term
| **Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment. |
|
Definition
|
|
Term
|
Definition
| lines that intersect at a common point |
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|
Term
|
Definition
| the point of intersection for concurrent lines |
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|
Term
|
Definition
| point of concurrency of the perpendicular bisectors of a triangle |
|
|
Term
|
Definition
| The circumcenter of a triangle is equidistant from the vertices of the triangle. |
|
|
Term
| **Any point on the angle bisector is equidistant from the sides of the angle. |
|
Definition
|
|
Term
| **Any point equidistant from the sides of an angle lies on the angle bisector. |
|
Definition
|
|
Term
|
Definition
| the point of concurrency for the angle bisectors of a triangle |
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|
Term
|
Definition
| segment whose endpoints are a vertex of a triangle and the midpoints of the side opposite the vertex |
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Term
|
Definition
| point of concurrency for the medians of a triangle |
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|
Term
|
Definition
| The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median. |
|
|
Term
|
Definition
| of a triangle, is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side |
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Term
|
Definition
| the intersection point of the altitudes of a triangle |
|
|
Term
| Exterior Angle Inequality Theorem |
|
Definition
| If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles. |
|
|
Term
| **If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. |
|
Definition
|
|
Term
| **If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. |
|
Definition
|
|
Term
|
Definition
| assume that the conclusion is false and then show that this assumption leads to a contradiction of the hypothesis, or some other accepted fact, such as definition, postulate, theorem, or corollary. |
|
|
Term
| Triangle Inequality Theorem |
|
Definition
| The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
|
|
Term
| **The perpendicular segment from a point to a line is the shortest segment from the point to the line. |
|
Definition
|
|
Term
| ****The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. |
|
Definition
|
|
Term
| SAS Inequality/Hinge Theorem |
|
Definition
| If two sides of a triangle are congruent to two sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, than the third side of the first triangle is longer than the third side of the second triangle. |
|
|
Term
|
Definition
| If two sides of a triangle are congruent to two sides of another triangle and the third side in one triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the second triangle. |
|
|
Term
|
Definition
| the top number of the first ratio, and the bottom number of the second ratio |
|
|
Term
|
Definition
| the bottom number of the first ratio, and the top number of the bottom ratio |
|
|
Term
| *Angle-Angle(AA) Similarity |
|
Definition
| If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. |
|
|
Term
| **Side-Side-Side(SSS) Similarity |
|
Definition
| If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar. |
|
|
Term
| **Side-Angle-Side(SAS) Similarity |
|
Definition
| If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. |
|
|
Term
| Triangle Proportionality Theorem |
|
Definition
| If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths. |
|
|
Term
| Triangle Midsegment Theorem |
|
Definition
| A segment of a triangle is parallel to one side of a triangle, and its length is one-half the length of that side. |
|
|
Term
| ****If three or more parallel intersect two transversals, then they cut off the transversals proportionality. |
|
Definition
|
|
Term
| ****If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. |
|
Definition
|
|
Term
| Proportional Perimeters Theorem |
|
Definition
| If two triangles are similar, then the perimeters are proportional to the measures of corresponding sides. |
|
|
Term
| **If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides. |
|
Definition
|
|
Term
| **If two triangles are similar, then the measures of the corresponding angle bisectors of the measures of the corresponding sides. |
|
Definition
|
|
Term
| **If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides. |
|
Definition
|
|
Term
|
Definition
| An angle bisector in a triangle separates the opposite side into segments that have the same ratio of the other two sides. |
|
|
Term
|
Definition
| between two numbers, is the positive square root of their product |
|
|
Term
| **If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the given triangle and to each other. |
|
Definition
|
|
Term
| **The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse. |
|
Definition
|
|
Term
| **If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the measure of a leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg. |
|
Definition
|
|
Term
|
Definition
| In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. |
|
|
Term
| Converse of the Pythagorean Theorem |
|
Definition
| If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. |
|
|
Term
|
Definition
| three whole numbers that satisfy the equation [image], where c is the greatest number. |
|
|
Term
|
Definition
| In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. |
|
|
Term
| Converse of the Pythagorean Theorem |
|
Definition
| If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. |
|
|
Term
|
Definition
| three whole numbers that satisfy the equation |
|
|
Term
| **In a 45°-45°-90° triangle, the length of the hypotenuse is √2 times the length of a leg. |
|
Definition
|
|
Term
| **In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg. |
|
Definition
|
|
Term
|
Definition
In a right triangle,
the length of the opposite side
the length of the hypotenuse |
|
|
Term
|
Definition
In a right triangle,
the length of the adjacent side
the length of the hypotenuse |
|
|
Term
|
Definition
In a right triangle,
the length of the opposite side
the length of the adjacent side |
|
|
Term
|
Definition
| angle between the line of sight and the horizontal when an observer looks upward |
|
|
Term
|
Definition
|
|
Term
|
Definition
In any triangle,
a²=b²+c²-2ab(cosA) |
|
|
Term
| Interior Angle Sum Theorem |
|
Definition
| If a convex polygon has n sides and S is the sum of the measures of its interior angles, then S=180(n-2) |
|
|
Term
| Exterior Angle Sum Theorem |
|
Definition
| If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360. |
|
|
Term
|
Definition
| a quadrilateral with parallel opposite sides |
|
|
Term
| Properties of Parallelograms |
|
Definition
Opposite sides are ≅
Opposite ∠ are ≅
Consecutive ∠s are supplementary
If it has one right ∠, it has 4 right ∠s
The diagonals bisect each other
Each diagonal makes 2 ≅ Δ
A pair of sides is parallel and ≅ |
|
|
Term
|
Definition
| a quadrilateral with four right angles |
|
|
Term
| Properties of a Rectangle |
|
Definition
Properties of a Parallelogram
Diagonals are ≅ and bisect each other
Opposite Sides are parallel and ≅
Opposite ∠s are ≅
Consecutive ∠s are supplementary
All four ∠s are right ∠s |
|
|
Term
|
Definition
| a quadrilateral with all four sides congruent |
|
|
Term
|
Definition
Properties of a Parallelogram
Diagonals are ⊥
Each diagonal bisects a pair of opposite ∠s |
|
|
Term
|
Definition
| a quadrilateral that is both a rhombus and a rectangle |
|
|
Term
|
Definition
Properties of a Parallelogram
Properties of a Rectangle
Properties of a Rhombus |
|
|
Term
|
Definition
| a quadrilateral with exactly one pair of parallel sides |
|
|
Term
|
Definition
| a trapezoid with congruent legs |
|
|
Term
| Properties of Isosceles Trapezoids |
|
Definition
One pair of parallel sides
Both pairs of base ∠s are ≅
Diagonals are ≅ |
|
|
Term
| **The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases. |
|
Definition
|
|
Term
|
Definition
| a transformation representing a flip of a figure |
|
|
Term
|
Definition
| a line that can be drawn through a plane figure so that the figure on one side is the reflection image of the figure on the opposite side |
|
|
Term
|
Definition
| the common point of reflection for all points of a figure |
|
|
Term
|
Definition
| the locus of all points in a plane equidistant from a given point called the center of the circle |
|
|
Term
|
Definition
| a segment with endpoints that are on the circle |
|
|
Term
|
Definition
| a chord that passes through the center |
|
|
Term
|
Definition
| a segment with endpoints that are the center and a point on the circle |
|
|
Term
|
Definition
|
|
Term
|
Definition
| has the center of the circle as its vertex, and its sides contain two radii of the circle |
|
|
Term
| ***The sum of the measures of the central angles of a circle with no interior points in common is 360. |
|
Definition
|
|
Term
|
Definition
| a part of the circle that is defined by two endpoints |
|
|
Term
|
Definition
| an arc with a measure less than 180 |
|
|
Term
|
Definition
| an arc with a measure more than 180 |
|
|
Term
|
Definition
| an arc with a measure of 180 |
|
|
Term
| **In the same or in congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent. |
|
Definition
|
|
Term
|
Definition
| The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. |
|
|
Term
|
Definition
|
|
Term
| **In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. |
|
Definition
|
|
Term
|
Definition
| a polygon where all of its vertices on a circle |
|
|
Term
|
Definition
| a circle that has an inscribed polygon on it |
|
|
Term
| **In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. |
|
Definition
|
|
Term
| **In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. |
|
Definition
|
|
Term
|
Definition
| If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc (or the measure of the intercepted arc is twice the measure of the inscribed angle). |
|
|
Term
| **If two inscribed angles of a circle (or congruent circles) intercept congruent arcs of the same arc, then the angles are congruent. |
|
Definition
|
|
Term
| **If an inscribed angle intercepts a semicircle, the angle is a right angle. |
|
Definition
|
|
Term
| **If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. |
|
Definition
|
|
Term
|
Definition
| a line that intersects a circle in exactly one point |
|
|
Term
|
Definition
| the point that a tangent intercepts a circle |
|
|
Term
| **If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. |
|
Definition
|
|
Term
| **If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle. |
|
Definition
|
|
Term
| **If two segments from the same exterior point are tangent to a circle, then they are congruent. |
|
Definition
|
|
Term
|
Definition
| a line that intersects a circle in exactly two points |
|
|
Term
| **If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle. |
|
Definition
|
|
Term
| **If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc. |
|
Definition
|
|
Term
| **If two secants, a tangent and a secant, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. |
|
Definition
|
|
Term
| **If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal. |
|
Definition
|
|
Term
| **If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment. |
|
Definition
|
|
Term
| **If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measures of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment. |
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
| If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A=bh. |
|
|
Term
|
Definition
| If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then A=.5bh |
|
|
Term
|
Definition
| If a trapezoid has an area of A square units, bases of b1 units and b2 units, and a height of h units, then A=.5h(b1+b2) |
|
|
Term
|
Definition
| If a rhombus has an area of A square units, and diagonals of d1 and d2 units, then A-.5d1d2 |
|
|
Term
| *Congruent figures have equal areas. |
|
Definition
|
|
Term
|
Definition
| a segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon |
|
|
Term
| Area of a Regular Polygon |
|
Definition
| If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then A=.5Pa |
|
|
Term
|
Definition
| If a circle has an area of A square units and a radius of r units, then A=πr² |
|
|
Term
|
Definition
| a figure that cannot be classified into the specific shapes that we have studied |
|
|
Term
| *The area of a region is the sum of all of its nonoverlapping parts. |
|
Definition
|
|
Term
|
Definition
| a polygon that is not regular |
|
|
Term
|
Definition
| probabiliy that involves a geometric measure such as length or area |
|
|
Term
|
Definition
If a point in reigon A is chosen at random, then the probability that the point is in region B, which is in the interior of region A is
P(B) = area of region B
area of region A |
|
|
Term
|
Definition
| of a circle, a region of a circle bounded by a central angle and its intercepted arc |
|
|
Term
|
Definition
If a sector of a circle has an area of A square units, a central angle measuring N°m and a radius of r units, then A= N πr²
360 |
|
|
Term
|
Definition
| the region of a circle bounded by an arc and a chord |
|
|
Term
|
Definition
| the two-dimensional views of the top, left, front, and right sides of an object |
|
|
Term
| Corner View or Perspective View |
|
Definition
| the view of a figure from a corner |
|
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Term
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Definition
| a solid with all flat surfaces that encloses a single region of space |
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| each flat surface of a polyhedron |
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| a line segment where the faces of a polyhedron intersect |
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| a polyhedron with two parallel congruent faces called bases |
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| a prism with bases that are regular polygons |
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| a polyhedron with all faces (except for one) intersecting at one vertex |
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| a polyhedron where all of the faces are regular congruent polygons and ll of the edges are congruent |
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| the five regular polyhedra: tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron |
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| a solid with congruent circular bases in a pair of parallel planes |
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| a solid with a circular base and a vertex |
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| a set of points in space that are a given distance from a given point |
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| the intersecion of the plane and solid |
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| a two-dimensional figure that when folded forms the surfaces of a three-dimensional object |
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| the sum of the areas of each face of the solid |
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| that faces that are not bases |
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| the intersection of lateral faces |
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| a prism with lateral edges that are also altitudes |
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Definition
| a prism with lateral edges not perpendicular to the base |
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Definition
| L, the sum of the areas of the lateral faces |
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Definition
| If a right prism has a lateral area of L square units, a height of h units, and each base has a perimeter of P units, then L=Ph |
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Definition
| If the surface area of a right prism is T square units, its height is h units, and each base has an area of B square units and a perimeter of P units, then T=L+2B |
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| of a cyliner, is the segment with endpoints that are the centers of the circular bases |
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| a cylinder where the axis is also the altitude |
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| a cylinder where the axis is not the altitude |
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| Lateral Area of a Cylinder |
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Definition
| If a right cylinder has a lateral area of L square unit, a height of h units, and the bases have radii of r units, then L=2πrh |
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| Surface Area of a Cylinder |
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Definition
| If a right cylinder has a surface area of T square units, a height of h units, and the bases have radii of r units, then T=2πrh+2πr² |
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Definition
| a pyramid where the base is a regular polygon and the segment with endpoints that are the center of the base and the vertex is perpendicular to the base |
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Definition
| l, the height of each lateral face |
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| Lateral Area of a Regular Pyramid |
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Definition
| If a regular pyramid has a lateral area of L square units, a slant height of l units, and its base has a perimeter of P units, then L=.5Pl |
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| Surface Area of a Regular Pyramid |
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Definition
| If a regular pyramid has a surface area of T square units, a slant height of l units, and its base has a perimeter of P units and an area of B square units, then T=.5Pl+B |
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Definition
| a cone with an axis that is also an altitude |
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| a cone with an axis that is not an altitude |
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Definition
| If a right circular cone has a lateral area of L square units, a slant height of l units, and the radius of the base is r units, then L=πrl |
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Definition
| If a right circular cone has a surface area of T square units, a slant height of l units, and the radius of the base is r units, then T=πrl+πr² |
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Definition
| for a given sphere, the intersection of the sphere and a plane that contains the center of the sphere |
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| one of the two congruent parts into which a great circle seperates a sphere |
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| If a sphere has a surface area of T square units and a radius of r units, then T=4πr² |
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