Congruent Triangles

Front

What are congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

What is the symbol used to denote congruence in triangles?

Back

The symbol for congruence is '≅'. For example, if triangle ABC is congruent to triangle DEF, it is written as ΔABC ≅ ΔDEF.

Front

What are the criteria for triangle congruence?

Back

The 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

Explain the Side-Side-Side (SSS) congruence criterion.

Back

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

Front

Explain the Side-Angle-Side (SAS) congruence criterion.

Back

The SAS criterion 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

Explain the Angle-Side-Angle (ASA) congruence criterion.

Back

The ASA criterion 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

Explain the Angle-Angle-Side (AAS) congruence criterion.

Back

The AAS criterion 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 the Hypotenuse-Leg (HL) criterion for right triangles?

Back

The HL criterion states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

How can you prove that two triangles are congruent using the SSS criterion?

Back

To prove two triangles are congruent using the SSS criterion, measure the lengths of all three sides of both triangles and show that they are equal.

Front

What is the importance of congruent triangles in geometry?

Back

Congruent triangles are important in geometry because they help in solving problems related to shape, size, and area, and are used in proofs and constructions.