triangle congruence proofs

Front

What is triangle congruence?

Back

Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The main criteria for triangle congruence are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA), 4) Angle-Angle-Side (AAS), and 5) Hypotenuse-Leg (HL) for right triangles.

Front

Define SSS (Side-Side-Side) congruence criterion.

Back

SSS states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

Define SAS (Side-Angle-Side) congruence criterion.

Back

SAS states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

Define ASA (Angle-Side-Angle) congruence criterion.

Back

ASA states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

Define AAS (Angle-Angle-Side) congruence criterion.

Back

AAS states that 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, then the triangles are congruent.

Front

What is CPCTC?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent.' It is used to prove that corresponding angles and sides of congruent triangles are equal.

Front

What does it mean if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion, but they may not be the same size.

Front

What is the significance of a triangle's bisector?

Back

A triangle's bisector divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Front

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

Back

If triangle ABC is congruent to triangle DEF, then angle A = angle D, angle B = angle E, angle C = angle F, and side AB = side DE, side BC = side EF, side AC = side DF.