Triangle Congruence Statements

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the symbol '≅' represent in geometry?

Back

It represents that two figures are congruent.

Front

List the criteria for triangle congruence. (SAS, SSS, ASA, AAS, HL)

Back

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

Front

If ∆ABC ≅ ∆LMN, what can we conclude about the corresponding sides?

Back

AB ≅ LM, BC ≅ MN, AC ≅ LN.

Front

What is the Angle-Angle (AA) criterion for triangle similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What is the Side-Angle-Side (SAS) congruence criterion?

Back

If two sides of one triangle are equal to two sides of another triangle, and the included angle is equal, the triangles are congruent.

Front

What is the significance of the Hypotenuse-Leg (HL) theorem?

Back

It states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, the triangles are congruent.

Front

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

Back

By measuring all three sides of both triangles and confirming that they are equal.

Front

What does it mean if two angles are corresponding angles in congruent triangles?

Back

They are equal in measure and are in the same relative position in each triangle.

Front

If ∆XYZ ≅ ∆ABC, what can we say about the angles?

Back

∠X ≅ ∠A, ∠Y ≅ ∠B, ∠Z ≅ ∠C.