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Concept. ___. BCA is opposite BA and A is opposite BC , so BCA A. ___. Congruent Segments and Angles. A. Name two unmarked congruent angles. Answer: BCA and A. Example 1. ___. BC is opposite D and BD is opposite BCD , so BC BD. ___. ___. ___. ___.
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___ BCA is opposite BA and A is opposite BC, so BCA A. ___ Congruent Segments and Angles A. Name two unmarked congruent angles. Answer: BCAand A Example 1
___ BC is opposite D and BD is opposite BCD, so BC BD. ___ ___ ___ ___ Answer: BC BD Congruent Segments and Angles B. Name two unmarked congruent segments. Example 1
A. Which statement correctly names two congruent angles? A.PJM PMJ B.JMK JKM C.KJP JKP D.PML PLK Example 1a
A.JP PL B.PM PJ C.JK MK D.PM PK B. Which statement correctly names two congruent segments? Example 1b
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. Answer:mR = 60 Divide each side by 2. Example 2
Find Missing Measures B. 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 2
A. Find mT. A. 30° B. 45° C. 60° D. 65° Example 2a
B. Find TS. A. 1.5 B. 3.5 C. 4 D. 7 Example 2b
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 ALGEBRA Find the value of each variable. Example 3
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. Example 3
Find Missing Values 4 = y Divide each side by 2. Answer:x = 17, y = 4 Example 3
Find 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