4.1-4.7 Congruent Triangles

Front

What are congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What does the HL postulate state?

Back

The HL (Hypotenuse-Leg) postulate states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

What does the AAS postulate state?

Back

The AAS (Angle-Angle-Side) postulate 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 does the SSS postulate state?

Back

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

Front

What is the significance of common angles or sides in congruent triangles?

Back

Common angles or sides can help establish congruence between triangles, as they provide direct evidence of equality in corresponding parts.

Front

How can you find the value of x in congruent triangles?

Back

To find the value of x, you can set up equations based on the properties of congruent triangles, using corresponding sides or angles.

Front

What is the definition of corresponding sides in triangles?

Back

Corresponding sides are the sides of two triangles that are in the same relative position with respect to their angles.

Front

What is the definition of corresponding angles in triangles?

Back

Corresponding angles are the angles of two triangles that are in the same relative position with respect to their sides.

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is important in geometry because it allows us to prove that two triangles are identical, which can be used in various applications such as construction, design, and solving geometric problems.

Front

What is the difference between the AAS and ASA postulates?

Back

The AAS postulate involves two angles and a non-included side, while the ASA (Angle-Side-Angle) postulate involves two angles and the included side.