Congruent Triangles

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SAS postulate state?

Back

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 ASA postulate state?

Back

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

What does the AAS postulate state?

Back

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

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What is the HL postulate?

Back

The Hypotenuse-Leg (HL) theorem 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 triangles are congruent.

Front

How can you prove triangles are congruent using the SAS postulate?

Back

By showing that two sides and the angle between them in one triangle are equal to the corresponding two sides and angle in another triangle.

Front

What additional information is needed to prove triangles congruent by SAS?

Back

You need to know the measure of the included angle between the two sides.

Front

What is the significance of corresponding parts in congruent triangles?

Back

Corresponding parts of congruent triangles are equal, which means if triangles are proven congruent, all their corresponding sides and angles are also equal.

Front

How do you find the value of a variable in congruent triangles?

Back

Set the corresponding sides or angles equal to each other and solve for the variable.