Geometry Regents - Theorem Review Notes

Theorem #1: If 2 angles form a linear pair, then they are supplementary.

Unit 1

Theorem #2: If 2 angles are complementary to the same angle, they their measures are equal.

Theorem #3: If 2 angles are supplementary to the same angle, then their measures are equal.

Two angles are congruent if they have the equal measures.

Theorem #4: If 2 angles are vertical angles, then they are congruent.

Two triangles are congruent if their corresponding parts are congruent.

SSS Postulate: If 3 pairs of corresponding sides of 2 triangles are congruent then the two triangles are congruent.

ASA postulate: If 2 pairs of corresponding angles in the 2 triangles and the side in between them are congruent, then the 2 triangles are congruent.

SAS postulate: If 2 pairs of corresponding sides in the 2 triangles and the angle in between them are congruent, then the 2 triangles are congruent.

Theorem #5: All right angles are congruent

Theorem #6: Addition theorem of congruence

Theorem #7: Subtraction theorem of congruence

If 2 angles are congruent, then their corresponding parts are congruent.

AAS postulate: If two angles and the non-included side of one triangle are congruent the other, then the 2 triangles are congruent.

Theorem #8: If 2 supplementary angles are congruent, then they are right angles.

Hypotenuse-Leg Postulate: If the hypotenuse and a pair of legs in 2 right triangles are congruent, then the 2 triangles are congruent.

Theorem #9: (Base-Angle Theorem) If a triangle has 2 congruent sides, the 2 angles opposite those sides are congruent.

Isosceles Triangle Property (Little Theorem): If a triangle is isosceles, then its' median, angle bisector, and altitude coincide.

Theorem #10: A triangle is isosceles if its median, angle bisector, and altitude from the vertex angle coincide.

Unit 1