14
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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A. PJM PMJ
B. JMK JKM
C. KJP JKP
D. PML PLK
A. Which statement correctly names two congruent angles?
B. Which statement correctly names two congruent segments?
A. JP PL
B. PM PJ
C. JK MK
D. PM PK
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
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.
Find Missing Measures
B. Find PR.
Answer: PR = 5 cm
A. 30°
B. 45°
C. 60°
D. 65°
A. Find mT.
A. 1.5
B. 3.5
C. 4
D. 7
B. Find TS.
Find Missing Values
ALGEBRA Find the value of each variable.
Since 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
mDFE = 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.
Find Missing Values
4 = y Divide each side by 2.
Answer: x = 17, y = 4
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.
