Triangle Congruence Statements

Front

What does it mean when we say ∆ABC ≅ ∆XYZ?

Back

It means that the triangles ∆ABC and ∆XYZ are congruent, meaning they have the same shape and size, and their corresponding sides and angles are equal.

Front

What is the significance of the congruence statement AB ≅ XY?

Back

It indicates that side AB of triangle ∆ABC is equal in length to side XY of triangle ∆XYZ.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that shows that two geometric figures are congruent, listing corresponding parts in the same order.

Front

If ∠U ≅ ∠F, what can we conclude about these angles?

Back

We can conclude that angles ∠U and ∠F are equal in measure.

Front

What does the notation ∠E ≅ ∠A signify?

Back

It signifies that angle E is congruent to angle A, meaning they have the same angle measure.

Front

What is the purpose of using congruence statements in geometry?

Back

Congruence statements help in proving that two triangles or other geometric figures are identical in shape and size, which is essential for solving problems involving these figures.

Front

What are the three main triangle congruence criteria?

Back

The three main triangle congruence criteria are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA).

Front

How can you determine if two triangles are congruent using the SSS criterion?

Back

Two triangles are congruent using the SSS criterion if all three sides of one triangle are equal in length to the corresponding sides of the other triangle.

Front

What does the SAS criterion state?

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

What is the Angle-Angle-Side (AAS) 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.