ALL About Proving Triangles Congruent

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

List the criteria for triangle congruence. What are the main rules?

Back

The main rules 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

What is the SSS congruence criterion?

Back

The SSS (Side-Side-Side) criterion states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

Explain the SAS congruence criterion.

Back

The SAS (Side-Angle-Side) 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 ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which is a criterion that states if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

Define AAS in the context of triangle congruence.

Back

AAS stands for Angle-Angle-Side, which 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 (Hypotenuse-Leg) 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

Can two triangles be congruent if only one side is equal?

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle or other congruence criteria must be satisfied.

Front

What does it mean if triangles cannot be proven congruent?

Back

If triangles cannot be proven congruent, it means there is insufficient information or criteria to establish that the triangles are equal in size and shape.

Front

How can you determine if two triangles are not congruent?

Back

Two triangles are not congruent if any corresponding sides or angles are not equal, or if they do not meet any of the congruence criteria.