Proving Triangles Congruent

Front

What does congruent mean in geometry?

Back

Congruent means that two figures have the same shape and size.

Front

What are the three main criteria for proving triangles congruent?

Back

The three main criteria are: 1) Side-Angle-Side (SAS), 2) Angle-Side-Angle (ASA), 3) Angle-Angle-Side (AAS).

Front

What is the Side-Angle-Side (SAS) congruence postulate?

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 is the Angle-Side-Angle (ASA) congruence postulate?

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 Angle-Angle-Side (AAS) congruence theorem?

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

How do you find the measure of a missing angle in a triangle?

Back

Use the fact that the sum of the angles in a triangle is always 180 degrees.

Front

If m∠A = 2x + 10, m∠B = 5x - 3, and m∠C = 3x - 7, how do you find x?

Back

Set up the equation: (2x + 10) + (5x - 3) + (3x - 7) = 180 and solve for x.

Front

What is the definition of supplementary angles?

Back

Supplementary angles are two angles whose measures add up to 180 degrees.

Front

What is the definition of complementary angles?

Back

Complementary angles are two angles whose measures add up to 90 degrees.

Front

What is the difference between vertical angles and adjacent angles?

Back

Vertical angles are opposite angles formed by two intersecting lines and are always congruent. Adjacent angles share a common side and vertex but do not overlap.