You identified isosceles and equilateral triangles.

• Use properties of isosceles triangles.

• Use properties of equilateral triangles.

• legs of an isosceles triangle

• vertex angle

• base angles

Congruent Segments and Angles

A. Name two unmarked congruent angles.

Answer: BCA and A

BCA is opposite BA and A is opposite BC, so BCA A.

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Congruent Segments and Angles

B. Name two unmarked congruent segments.

Answer: BC BD

___BC is opposite D and BD is opposite BCD, so BC BD.

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Since 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.

Divide each side by 2.Answer: mR = 60

A. 30°

B. 45°

C. 60°

D. 65°

A. Find mT.

A. 1.5

B. 3.5

C. 4

D. 7

B. Find TS.

A. x = 20, y = 8

B. x = 20, y = 7

C. x = 30, y = 8

D. x = 30, y = 7

Find the value of each variable.