Solving Congruent Triangles

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 in triangles?

Back

The symbol for congruence is '≅'.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA), 4) Angle-Angle-Side (AAS), and 5) Hypotenuse-Leg (HL) for right triangles.

Front

If ∆ ABC ≅ ∆ DEF, what can we say about their corresponding angles?

Back

The corresponding angles of congruent triangles are equal, so ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F.

Front

If two triangles are congruent, what can we say about their corresponding sides?

Back

The corresponding sides of congruent triangles are equal in length.

Front

How can you determine the value of a variable in congruent triangles?

Back

You can set the corresponding sides or angles equal to each other and solve for the variable.

Front

What is the value of x if ∆ LET ≅ ∆ PIC and one corresponding side is 50?

Back

x = 50.

Front

What is the value of y if ∆ LET ≅ ∆ PIC and one corresponding angle is 15°?

Back

y = 15°.

Front

If ∆ MAP ≅ ∆ EHP and the corresponding side measures 11, what is the value of x?

Back

x = 11.

Front

What is the measure of ∠ M if ∆ POT ≅ ∆ SUM and ∠ M = 75°?

Back

∠ M = 75°.