#3 Proving Triangles Congruent Mini-Flashcard

Front

What is triangle congruence?

Back

Triangle congruence means that two triangles are congruent if they have the same size and shape, which can be proven using specific criteria.

Front

List the criteria for triangle congruence.

Back

1. Side-Side-Side (SSS) Congruence 2. Side-Angle-Side (SAS) Congruence 3. Angle-Side-Angle (ASA) Congruence 4. Angle-Angle-Side (AAS) Congruence 5. Hypotenuse-Leg (HL) Congruence (for right triangles)

Front

What does SSS stand for in triangle congruence?

Back

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

Front

Explain SAS congruence criterion.

Back

SAS stands for Side-Angle-Side. It 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

What is the ASA criterion for triangle congruence?

Back

ASA stands for Angle-Side-Angle. It 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 in the context of triangle congruence.

Back

AAS stands for Angle-Angle-Side. It 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?

Back

The Hypotenuse-Leg (HL) criterion applies to right triangles. It states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

How can you prove 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. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they allow us to establish that certain properties, such as angles and sides, are equal, which can be used in proofs and problem-solving.

Front

Provide an example of using the SAS criterion to prove triangle congruence.

Back

If triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60°, and triangle DEF has sides DE = 5 cm, DF = 7 cm, and angle D = 60°, then triangles ABC and DEF are congruent by SAS.