Congruence

Front

What is congruence in geometry?

Back

Congruence in geometry means that two figures have the same shape and size. If two shapes are congruent, they can be made to coincide by rigid transformations such as translation, rotation, or reflection.

Front

What is the symbol for congruence?

Back

The symbol for congruence is '≅'.

Front

If ΔABC ≅ ΔDEF, what can we say about their corresponding angles and sides?

Back

The corresponding angles and sides of congruent triangles are equal. For example, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F and AB = DE, BC = EF, AC = DF.

Front

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

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 congruent.

Front

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

Back

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

Front

What is the Side-Angle-Side (SAS) criterion for triangle congruence?

Back

The Side-Angle-Side (SAS) criterion states that 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) criterion for triangle congruence?

Back

The Angle-Side-Angle (ASA) criterion states that 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 it mean if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion, but they may not be the same size.

Front

How do you denote corresponding sides in congruent triangles?

Back

In congruent triangles, corresponding sides are denoted by the same letters. For example, if ΔABC ≅ ΔDEF, then AB corresponds to DE, BC corresponds to EF, and AC corresponds to DF.

Front

If ∠B = 2x and ∠Q = 10 in triangles ΔBAC and ΔQPR, how do you find x?

Back

Set up the equation 2x = 10. Solving for x gives x = 5.