TRIANGLES: Theorems and Postulates for Geometry
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15 terms
Terms | Definitions |
|---|---|
 Side-Side-Side (SSS) Congruence | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. |
| Side-Angle-Side (SAS) Congruence | If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
| Angle-Side-Angle (ASA) Congruence | If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
| Angle-Angle-Side (AAS) Congruence | If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
| Hypotenuse-Leg (HL) Congruence (right triangle) | If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. |
| CPCTC | Corresponding parts of congruent triangles are congruent. |
| Angle-Angle (AA) Similarity | If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. |
| SSS for Similarity | If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. |
| SAS for Similarity | If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. |
| Side Proportionality | If two triangles are similar, the corresponding sides are in proportion. |
| Mid-segment/Mid-line Theorem | The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. |
| Sum of Two Sides | The sum of the lengths of any two sides of a triangle must be greater than the third side |
| Longest Side | In a triangle, the longest side is across from the largest angle. In a triangle, the largest angle is across from the longest side. |
| Altitude Rule | The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. |
| Leg Rule | Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. |
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