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A. Which statement correctly names two congruent angles?

A.PJM PMJ

B.JMK JKM

C.KJP JKP

D.PML PLK

Example 1aSince QP = QR, QP QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR.

Find Missing Measures

A. Find mR.

Triangle Sum Theorem

mQ = 60, mP = mR

Simplify.

Subtract 60 from each side.

Answer:mR = 60

Divide each side by 2.

Example 2B. Find PR.

Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution.

Answer:PR = 5 cm

Example 2Since E = F, DE FE by the Converse of the Isosceles Triangle Theorem. DF FE, so all of the sides of the triangle are congruent. The triangle is equilateral. Each angle of an equilateral triangle measures 60°.

Find Missing Values

ALGEBRA Find the value of each variable.

Example 3mDFE = 60 Definition of equilateral triangle

4x – 8 = 60 Substitution

4x = 68 Add 8 to each side.

x = 17 Divide each side by 4.

The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal.

DF = FE Definition of equilateral triangle

6y + 3 = 8y – 5 Substitution

3 = 2y – 5 Subtract 6y from each side.

8 = 2y Add 5 to each side.

Example 3Find the value of each variable.

A.x = 20, y = 8

B.x = 20, y = 7

C.x = 30, y = 8

D.x = 30, y = 7

Example 3
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