Triangle Congruence Theorems

Front

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

Back

The AAS Congruence Theorem states that if two angles and the 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 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 corresponding 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 corresponding included angle of another triangle, then the two triangles are congruent.

Front

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 is the SSA (Side-Side-Angle) condition?

Back

The SSA condition does not guarantee triangle congruence. It can lead to ambiguous cases where two different triangles can be formed.

Front

What is the AAA (Angle-Angle-Angle) condition?

Back

The AAA condition indicates that if three angles of one triangle are congruent to three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

How do you denote congruent triangles?

Back

Congruent triangles are denoted using the symbol '≅'. For example, if triangle ABC is congruent to triangle DEF, it is written as △ABC ≅ △DEF.

Front

What is the significance of the included angle in triangle congruence?

Back

The included angle is the angle formed between two sides of a triangle. It is crucial in the ASA and SAS theorems for establishing triangle congruence.

Front

How can you prove two triangles are congruent using AAS?

Back

To prove two triangles are congruent using AAS, you need to show that two angles and a non-included side of one triangle are congruent to the corresponding parts of the other triangle.

Front

What additional information is needed to prove triangles are congruent by AAS?

Back

You need to show that one pair of corresponding angles is congruent and one pair of corresponding non-included sides is congruent.