enVision Geometry Unit 1-4 Theorems

Vertical Angles Theorem

If two angles are vertical angles, then they are congruent.

Linear Pair Theorem

If two angles form a linear pair, then they are supplementary.

Congruent Supplements Theorem

If two angles are supplementary to the same angle (or congruent angles), then they are congruent.

Congruent Complements Theorem

If two angles are complementary to the same angle (or congruent angles), then they are congruent.

Right Angle Theorem

If two angles are right angles, then they are congruent.

Corresponding Angles Postulate

If parallel lines are cut by a transversal, then corresponding angles are congruent.

Converse Corresponding Angles Theorem

If corresponding angles are congruent, then the lines are parallel.

Alternate Interior Angles Theorem

If parallel lines are cut by a transversal, then alternate interior angles are congruent.

Converse Alternate Interior Angles Theorem

If alternate interior angles are congruent, then the lines are parallel.

Alternate Exterior Angles Theorem

If parallel lines are cut by a transversal, then alternate exterior angles are congruent.

Converse Alternate Exterior Angles Theorem

If alternate exterior angles are congruent, then the lines are parallel.

Same-Side Interior Angles Theorem

If parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Converse Same-Side Interior Angles Theorem

If same-side interior angles are supplementary, then the lines are parallel.

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Converse Perpendicular Transversal Theorem

If two coplanar lines are perpendicular to the same line, then they are parallel.

Triangle Sum Theorem

The measures of the interior angles of a triangle add to 180 degrees.

Exterior Angle Theorem

The measure of an exterior angle equals the sum of the two remote interior angles.

SSS Congruence Postulate

If three pairs of corresponding sides are congruent, then the triangles are congruent.

SAS Congruence Postulate

If two sides and the included angle are congruent, then the triangles are congruent.

ASA Congruence Theorem

If two angles and the included side are congruent, then the triangles are congruent.

AAS Congruence Theorem

If two angles and a non-included side are congruent, then the triangles are congruent.

HL Theorem

If right triangles have congruent hypotenuses and one congruent leg, then the triangles are congruent.

CPCTC

If triangles are congruent, then corresponding parts are congruent.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the opposite angles are congruent.

Converse Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the opposite sides are congruent.

Equilateral Triangle Theorem

If a triangle is equilateral, then it is equiangular.

Converse Equilateral Triangle Theorem

If a triangle is equiangular, then it is equilateral.