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Through any three noncollinear points thre exists exactly one _______ |
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| If two planes intersect, there intersection is a _______ |
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A plane contains at least ______ noncollinear points. |
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| Right Angles Congruence Theorem |
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| All right angles are congruent |
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| If two angles form a linear pair, then they are supplementary |
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Vertical Angles Congruence Theorem (VACT) |
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| Vertical angles are congruent |
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| If there is a line and a point not on that line, then there are exactly how many lines through the point parallel to the given line? |
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If there is a line and a point not on that line, then there are how many lines going through that point that are perpendicular to the given line? |
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(name the postualte) If two parallel lines are cut by a transversal, then the pair of corresponding angles are congruent. |
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| Corresponding angles postulate |
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(name the postulate) If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. |
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| Alternate Interior Angles Theorem |
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(name the postulate) If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. |
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| Alternate Exterior Angles Theorem |
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(name the postulate) If two parallel lines are cut by a transeveral, then the pairs of consecutive interior angles are supplementary. |
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| Consecutive Interior Angles Theorem |
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What is the Corresponding Angles Converse Theorem? |
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| If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel. |
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What is the Alternate Interior Angles Converse Theorem? |
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Definition
| If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. |
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| What is the Alternate Exterior Angles Converse Theorem? |
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| If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel. |
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| What is the Consecutive Interior Angles Converse Theorem? |
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Definition
| If two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are parallel. |
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Use variables to explain the Transitive property. |
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Definition
| If a=b, and b=c, then a=c. |
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On a coordinate plane, if two nonvertical lines have the same slope, what does it mean? |
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Definition
| The two lines are parallel. |
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On a coordinate plane, what does it mean if the product of two nonvertical lines slopes is -1? |
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Definition
| The two lines are Perpendicular. |
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(name the Theorem) If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other as well. |
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| The Perpendicular Transversal Theorem. |
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(name the theorem) In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. |
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Definition
Lines Perpendicular to a Transversal Theorem. |
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What is the Triangle Sum Theorem? |
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Definition
| The sum of the measures of the interior angles of a triangle is 180*. |
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| What is the Exterior Angle Theorem? |
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Definition
| The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. |
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| What is the Third Angle Theorem? |
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Definition
| If two angles of one triangle are congruent to two angles of another triangle, then the third angles of those triangles are also congruent. |
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What is the Side-Side-Side congruence postulate? (SSS) |
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Definition
| If three sides of one triangle are congruent to three sides of another triangle then the two triangles are congruent to each other. |
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| Use variables to explain the reflexive property. |
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Definition
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What is the Side-Angle-Side Congruence postulate? (SAS) |
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Definition
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent to each other. |
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(name the theorem) If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and a leg of another triangle, then those two triangles are congruent to each other. |
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Definition
| Hypotenuse-Leg (HL) Congruence Theorem. |
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| what is the Angle-Side-Angle(ASA) Congruence Theorem? |
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Definition
| if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. |
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| What is the Angle-Angle-Side(AAS)Congruence Postulate? |
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Definition
| if two anglse and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent. |
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| What is the Base Angles Theorem? |
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Definition
| If two sides of a triangle are congruent, then the angles oppsite them are congruent. |
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| What is the Converse of the Base Angles Theorem? |
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Definition
| if two angles of a triangle are congruent, then the sides opposite them are congruent. |
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| What is the Midsegment Theorem? |
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Definition
| The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. |
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| What is the Perpendicular Bisector Theorem? |
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Definition
| In a plane, if a point is on the perpindicular bisector of a segment, then it is equidistant from the endpoints of the segment. |
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| What is the Converse of the Perpendicular Bisector Theorem? |
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Definition
| In a plane, if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |
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What is the Concurrency of Perpendicular Bisectors of a Triangle Theorem? |
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Definition
| The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. |
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| What is the Angle Bisector Theorem? |
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Definition
| If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. |
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| what is the converse of the Angle Bisector Theorem? |
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Definition
| If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. |
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| What is the Concurrency of Medians of a Triangle Theorem? |
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Definition
| The medians of a triangle intersect at a point that is two thrids of the distance from each vertex to the midpoint of the opposite side. |
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| What is the Concurrency of Altitudes of a Triangle Theorem? |
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Definition
| The lines containing the altitudes of a triangle are concurrent. |
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| Use variables to explain the Triangle Inequality Theorem. |
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Definition
in triange ABC the following must be true: AB+BC>AC AC+BC>AB AB+AC>BC |
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What is the Perimeters of Similar Polygons Theorem? |
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Definition
| if two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding lengths. |
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| What is the Angle-Angle (AA) Similarity Postualte? |
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Definition
| if two angles of one triangle are congruent to two angles of another triangle, then those two triangles are congruent to each other. |
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| What is the Side-Side-Side (SSS) Similarity Theorem? |
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Definition
| if the corresponding side lengths of two triangles are proportional, then the triangles are congruent. |
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What is the Triangle Proportionality Theorem? |
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Definition
| if a line parallel to one side of a triangle intersents the other two sides, then it divides the two sides proportionally. |
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| What is the converse of the Triangle Proportionality Theorem? |
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Definition
| if a line divides two sides of a triangle proportionally, then it is parallel to the third side. |
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If three parallel lines intersect two transversals, then ___________________________. |
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Definition
| They divide the transversals proportionally. |
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| If a ray bisects an angle of a triangle, then ____________________________. |
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Definition
| it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. |
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