Triangles: Congruence and Corresponding Parts

Front

What is a triangle?

Back

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Front

What does it mean for triangles to be congruent?

Back

Triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What are the different methods to prove triangle congruence?

Back

The methods to prove triangle congruence include SSS (Side-Side-Side), SAS (Side-Angle-Side), AAS (Angle-Angle-Side), ASA (Angle-Side-Angle), and HL (Hypotenuse-Leg for right triangles).

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which means if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which means if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which means if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which means if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, which is a method used to prove the congruence of right triangles by showing that the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle.

Front

How can you identify corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the sides and angles that are in the same position in each triangle. For example, if triangle ABC is congruent to triangle DEF, then angle A corresponds to angle D, side AB corresponds to side DE, and so on.

Front

If triangle ABC is congruent to triangle DEF, what can be said about their angles and sides?

Back

If triangle ABC is congruent to triangle DEF, then all corresponding angles are equal (∠A = ∠D, ∠B = ∠E, ∠C = ∠F) and all corresponding sides are equal (AB = DE, BC = EF, AC = DF).