Triangle Congruence Theorems

Front

What is the ASA (Angle-Side-Angle) Congruence Theorem?

Back

The ASA Congruence Theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Congruence Theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What is the SAS (Side-Angle-Side) Congruence Theorem?

Back

The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What is the SSS (Side-Side-Side) Congruence Theorem?

Back

The SSS Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

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What is the HL (Hypotenuse-Leg) Congruence Theorem?

Back

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

Front

What does SSA (Side-Side-Angle) mean in triangle congruence?

Back

SSA is not a valid method for proving triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

What is the difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side. Both can be used to prove triangle congruence.

Front

How can you prove triangles are congruent using the SSS theorem?

Back

To prove triangles are congruent using SSS, show that all three corresponding sides of the triangles are equal in length.

Front

What is the significance of the included angle in the SAS theorem?

Back

The included angle in the SAS theorem is crucial because it is the angle formed between the two sides being compared, ensuring the triangles are congruent.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, often written as △ABC ≅ △DEF.