Test Review: Triangle Congruency

Front

What is Triangle Congruency?

Back

Triangle congruency refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruency?

Back

The criteria for triangle congruency include: 1. Side-Side-Side (SSS) - all three sides are equal. 2. Side-Angle-Side (SAS) - two sides and the included angle are equal. 3. Angle-Side-Angle (ASA) - two angles and the included side are equal. 4. Angle-Angle-Side (AAS) - two angles and a non-included side are equal. 5. Hypotenuse-Leg (HL) - for right triangles, the hypotenuse and one leg are equal.

Front

If two triangles have two equal angles, what can be said about their sides?

Back

If two triangles have two equal angles, the third angle must also be equal, and the triangles are similar. However, the sides may not be equal unless the triangles are also congruent.

Front

What does the Side-Angle-Side (SAS) criterion state?

Back

The SAS criterion states that if two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides is also equal, then the two triangles are congruent.

Front

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

Back

To find the measure of an angle in a triangle, you can use the fact that the sum of the interior angles in a triangle is always 180 degrees. If you know the measures of the other two angles, subtract their sum from 180 degrees.

Front

What is the significance of the Hypotenuse-Leg (HL) theorem?

Back

The HL theorem states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the two triangles are congruent.

Front

What is the Angle-Side-Angle (ASA) criterion?

Back

The ASA criterion states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.

Front

What is the difference between congruent and similar triangles?

Back

Congruent triangles are identical in shape and size, with equal corresponding sides and angles. Similar triangles have the same shape but may differ in size, with corresponding angles equal and sides in proportion.

Front

How can you prove that two triangles are congruent?

Back

To prove that two triangles are congruent, you can use one of the congruency criteria: SSS, SAS, ASA, AAS, or HL. You need to show that the corresponding sides and angles meet the conditions of one of these criteria.

Front

What is the purpose of using congruency in geometry?

Back

The purpose of using congruency in geometry is to establish relationships between shapes, allowing for the determination of unknown lengths and angles, and to prove geometric theorems.