Congruent Triangles Practice

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the symbol used to denote congruence between two triangles?

Back

The symbol for congruence is '≅'. For example, if triangle ABC is congruent to triangle DEF, it is written as ΔABC ≅ ΔDEF.

Front

What are the criteria for triangle congruence?

Back

The main criteria for triangle congruence are: 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 ΔABC ≅ ΔDEF, what can we say about their corresponding angles?

Back

If ΔABC ≅ ΔDEF, then the corresponding angles are also equal. For example, ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F.

Front

What is the Angle-Angle (AA) criterion for triangle similarity?

Back

The Angle-Angle (AA) criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar, which means their corresponding sides are in proportion.

Front

How can you prove that two triangles are congruent using the SAS criterion?

Back

To prove two triangles are congruent using the SAS criterion, you need to show that two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that two triangles are identical in size and shape, while similarity means that two triangles have the same shape but may differ in size. Similar triangles have proportional sides and equal corresponding angles.

Front

If two triangles have two pairs of equal angles, what can be concluded about them?

Back

If two triangles have two pairs of equal angles, they are similar by the Angle-Angle (AA) criterion. However, they may not be congruent unless the third angle is also equal.

Front

What is the Side-Side-Side (SSS) congruence criterion?

Back

The Side-Side-Side (SSS) congruence criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

How do you denote the corresponding sides of congruent triangles?

Back

The corresponding sides of congruent triangles are denoted by matching letters. For example, if ΔABC ≅ ΔDEF, then side AB corresponds to side DE, side BC corresponds to side EF, and side CA corresponds to side FD.