Triangle Proof Theorems

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 ASA congruence theorem 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 SAS congruence theorem 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 SSS congruence theorem 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 significance of the included angle in the SAS theorem?

Back

The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence.

Front

How can you determine if two triangles are congruent using the SSS theorem?

Back

Measure the lengths of all three sides of both triangles; if all three pairs of sides are equal, the triangles are congruent.

Front

What additional information is needed to prove congruence using SSS?

Back

You need to know the lengths of all three sides of both triangles.

Front

What is the difference between ASA and AAS congruence theorems?

Back

ASA requires the included side, while AAS uses two angles and a non-included side.

Front

What is the definition of an included angle?

Back

An included angle is the angle formed between two sides of a triangle.

Front

What is the purpose of triangle congruence theorems?

Back

To establish that two triangles are identical in shape and size, allowing for the application of various geometric principles.