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Concept

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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Concept

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  1. Concept

  2. ___ 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

  3. ___ 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

  4. A. Which statement correctly names two congruent angles? A.PJM PMJ B.JMK JKM C.KJP JKP D.PML PLK Example 1a

  5. A.JP PL B.PM PJ C.JK MK D.PM PK B. Which statement correctly names two congruent segments? Example 1b

  6. Concept

  7. Since QP = QR, QP  QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR. Find Missing Measures A. Find mR. Triangle Sum Theorem mQ = 60, mP = mR Simplify. Subtract 60 from each side. Answer:mR = 60 Divide each side by 2. Example 2

  8. 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

  9. A. Find mT. A. 30° B. 45° C. 60° D. 65° Example 2a

  10. B. Find TS. A. 1.5 B. 3.5 C. 4 D. 7 Example 2b

  11. 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

  12. Find Missing Values mDFE = 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

  13. Find Missing Values 4 = y Divide each side by 2. Answer:x = 17, y = 4 Example 3

  14. 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

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