Triangle Congruence Statements

Front

What does the symbol '≅' represent in geometry?

Back

The symbol '≅' represents that two geometric figures are congruent, meaning they have the same shape and size.

Front

What are the criteria for triangle congruence?

Back

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

Front

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

Back

If ∆ABC ≅ ∆LMN, then AB ≅ LM, BC ≅ MN, AC ≅ LN, ∠A ≅ ∠L, ∠B ≅ ∠M, and ∠C ≅ ∠N.

Front

What is the meaning of the term 'corresponding parts' in triangle congruence?

Back

'Corresponding parts' refer to the sides and angles of congruent triangles that match each other in position.

Front

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

Back

To determine if two triangles are congruent using the SSS criterion, check if all three sides of one triangle are equal to the three sides of the other triangle.

Front

What is the SAS criterion for triangle congruence?

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 does the AAS criterion for triangle congruence state?

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 HL criterion for triangle congruence?

Back

The HL criterion applies to right triangles and 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

If ∆DEF ≅ ∆FED, what can we say about their corresponding angles?

Back

If ∆DEF ≅ ∆FED, then ∠D ≅ ∠F, ∠E ≅ ∠E, and ∠F ≅ ∠D.

Front

What is the significance of congruence statements in geometry?

Back

Congruence statements provide a way to express that two figures are identical in shape and size, allowing for the transfer of properties from one figure to another.