Explore Triangle Congruence 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 are the three main triangle congruence theorems?

Back

1. Side-Side-Side (SSS) Congruence Theorem 2. Side-Angle-Side (SAS) Congruence Theorem 3. Angle-Side-Angle (ASA) Congruence Theorem.

Front

Explain the Side-Side-Side (SSS) Congruence Theorem.

Back

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

Front

Explain the Side-Angle-Side (SAS) Congruence Theorem.

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

Explain the Angle-Side-Angle (ASA) Congruence Theorem.

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 is the Hypotenuse-Leg (HL) Theorem for right triangles?

Back

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

What does it mean for triangles to be similar?

Back

Triangles that have the same shape but not necessarily the same size; their corresponding angles are equal, and their corresponding sides are in proportion.

Front

How can you prove that two triangles are congruent using the SSS theorem?

Back

Measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is fundamental in proving properties of geometric figures, solving problems, and establishing relationships between different shapes.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means triangles are identical in size and shape, while similarity means they have the same shape but may differ in size.