Unit 4 - Congruent Triangles

Congruent Supplements Theorem

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

Congruent Complements Theorem

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

The point where two sides come together

Vertex

Two sides of a triangle that share a common vertex

Adjacent sides

The side opposite of an angle; does not share the same vertex

Opposite side

Three angles inside a triangle

Interior angles

Angles adjacent to interior angles

Exterior angles

Triangle Sum Theorem

The sum of the measure of the interior angles of a triangle is 180 degrees

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of two nonadjacent angles

Third Angles Theorem

If two angles of a triangle are congruent to two angles of a second triangle, then the third angles are congruent.

SSS

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS

If two sides and an included angle of one triangle are congruent to two sides and an included angle of another triangle, then the triangles are congruent.

ASA

If two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the triangles are congruent.

AAS

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 triangles are congruent.

HL

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

Distance formula

Midpoint formula