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Geometry.Campo-5#
Theorems and Angles (Proofs)
| Term | Definition |
|---|---|
| Vertical Angles Theorem | If two angles are vertical, then they are congruent. |
| Complement Theorem | If two angles form a right angle, then they are complementary. Right Angle -> Complementary |
| Supplement Theorem | If two angles form a linear pair, then they are supplementary. Linear pair -> Supplementary |
| Congruent Complements Theorem | If ∠A is complementary to ∠B and ∠C is complementary to ∠B, then ∠A is congruent to ∠C |
| Congruent Supplements Theorem | If ∠A is complementary to ∠B and ∠C is supplementary to ∠B, then ∠A is congruent to ∠C |
| (Unit 2) Corresponding Angles | Angles that match size and position when based on a traversal cutting through two parallel lines. |
| Alternate Exterior Angles | Alternating sides of the Transversal on exterior of the parallel lines. |
| Alternate Interior Angles | Alternating sides of the Transversal on interior of the parallel lines. |
| Same side interior Angles | Same sides of the Transversal on inside of the parallel lines. |
| Same side exterior Angles | Same sides of the transversal on the outside of the parallel lines. |
| Same side interior/exterior angle Theorem | If a transversal intersects two parallel lines, the the same side interior angles are supplementary. |
| Alternate Interior Angle Theorem | If a transversal intersects two parallel lines, then alternate interior angles are congruent. |
| Alternate Exterior Angle Theorem | If a transversal intersects two parallel lines, then alternate Exterior Angles are congruent. |
| Corresponding Angles Theorem | If a transversal intersects two parallel lines, then Corresponding angles are congruent. |
| Converse of Coresponding Angles Theorem | If two lines and a transversal form corresponding Angles that are congruent, then the lines are parallel. |
| Converse of Alternate Interior Angles Theorem | If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel. |
| Converse of same side interior angles Theorem | If two lines and a transversal form same side angles that are supplementary, then the lines are parallel. |
| Converse of alternate Exterior angles Theorem | If two lines and a transversal form alternate Exterior angles that are congruent, then the lines are parallel. |
| Triangle angle sum Theorem | The sum of the measures of all the angles of a triangle is 180 degrees. |
| (Unit 4) Isosceles Triangle Theorem | If two sides of a triangle are congruent, then the angles opposite those sides are congruent. |
| Converse of Isosceles Triangle Theorem | If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
| Theorem 4-2 | The angle bisector of the vertex angle of an isosceles triangle is also the perpendicular bisector of the base. |
| Theorem 4-3 Side-Angle-Side (SAS) Congruence Criterion | If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. |
| Theorem 4-4 Corresponding Parts of Congruence Triangles are Congruent (CPCTC) | If two triangles are congruent, then each pair of Corresponding sides is congruent and each pair of Corresponding angles is congruent. |
| Theorem 4-5 Side-Side-Side (SSS) Congruence Criterion | If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. |
| Theorem 4-6 Angle-Side-Angle (ASA) Congruence Criterion | If two angles of one triangle and the included side are congruent to two angles and included side of another triangle, then the two triangles are congruent. |
| Theorem 4-7 Angle-Angle-Side (AAS) Congruence Criterion | If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the two triangles are congruent. |
| (Unit 5) Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints on a segment. |
| Converse of Perpendicular Bisector Theorem | If a point is equidistant from the endpoints of a segment, then it must lie on the perpendicular bisector of the segment. |
| Angle Bisector Theorem | If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. |
| Converse of Angle Bisector Theorem | If a point is equidistant from the sides of an angle, then it is on the angle bisector of the angle. |
| Theorem 5-9 | If two sides of a triangle are not congruent, then the larger angle lies opposite the largest side. |
| Converse of Theorem 5-9 | If two angles of a triangle are not congruent, then the longer side lies opposite the largest angle. |
| Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle must be greater than the third side. |
| Hinge Theorem | If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is opposite the larger included angle. |
| Converse of Hinge Theorem | If two sides of one triangle are not congruent to two sides of another and the third sides are not congruent, then the larger included angle is opposite the longer third side. |
Created by:
PaigeRyals-9th
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