geometry Module 5

Sum of interior angles of a triangle

The sum of the measures of the interior angles of a triangle is 180 degrees.

Exterior angle of a triangle

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

Congruent figures

Two figures are congruent if there is a rigid transformation that maps one figure exactly onto the other.

Congruent polygons

In two congruent polygons, all the parts of one polygon are congruent to the corresponding parts of the other polygon.

SSS (Side-Side-Side) Congruence

Three sides of one triangle are congruent to three sides of a second triangle.

SAS (Side-Angle-Side) Congruence

Two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle.

ASA (Angle-Side-Angle) Congruence

Two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle.

AAS (Angle-Angle-Side) Congruence

Two angles and the non-included side of one triangle are congruent to two angles and the non-included side of a second triangle.

Leg-Leg Congruence (LL)

In right triangles, congruence can be proved if the legs are congruent.

Hypotenuse-Angle Congruence (HA)

In right triangles, congruence can be proved if the hypotenuse and an angle are congruent.

Leg-Angle Congruence (LA)

In right triangles, congruence can be proved if a leg and an angle are congruent.

Hypotenuse-Leg Congruence (HL)

In right triangles, congruence can be proved if the hypotenuse and one leg are congruent.

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.

Equilateral Triangle

Each angle of an equilateral triangle measures 60 degrees.

Coordinate Proof

To write a coordinate proof, place the figure on the coordinate plane, label the vertices, and use algebra to prove properties of theorems.