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Splash Screen. Find m 1. A. 115 B. 105 C. 75 D. 65. 5-Minute Check 1. Find m 2. A. 75 B. 72 C. 57 D. 40. 5-Minute Check 2. Find m 3. A. 75 B. 72 C. 57 D. 40. 5-Minute Check 3. Find m 4. A. 18 B. 28 C. 50 D. 75. 5-Minute Check 4. Find m 5. A. 70

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  1. Splash Screen

  2. Find m1. A. 115 B. 105 C. 75 D. 65 5-Minute Check 1

  3. Find m2. A. 75 B. 72 C. 57 D. 40 5-Minute Check 2

  4. Find m3. A. 75 B. 72 C. 57 D. 40 5-Minute Check 3

  5. Find m4. A. 18 B. 28 C. 50 D. 75 5-Minute Check 4

  6. Find m5. A. 70 B. 90 C. 122 D. 140 5-Minute Check 5

  7. One angle in an isosceles triangle has a measure of 80°. What is the measure of one of the other two angles? A. 35 B. 40 C. 50 D. 100 5-Minute Check 6

  8. congruent • congruent polygons • corresponding parts Vocabulary

  9. Concept 1

  10. Angles: Sides: Identify Corresponding Congruent Parts Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ. Example 1

  11. A. B. C. D. The support beams on the fence form congruent triangles. In the figure ΔABC ΔDEF,which of the following congruence statements correctly identifies corresponding angles or sides? Example 1

  12. Use Corresponding Parts of Congruent Triangles In the diagram, ΔITP ΔNGO. Find the values of x and y. O  P CPCTC mO = mP Definition of congruence 6y – 14 = 40 Substitution Example 2

  13. CPCTC Use Corresponding Parts of Congruent Triangles 6y = 54Add 14 to each side. y= 9Divide each side by 6. NG= ITDefinition of congruence x – 2y = 7.5 Substitution x – 2(9) = 7.5 y = 9 x – 18 = 7.5 Simplify. x= 25.5Add 18 to each side. Answer:x = 25.5, y = 9 Example 2

  14. In the diagram, ΔFHJ ΔHFG. Find the values of x and y. A.x = 4.5, y = 2.75 B.x = 2.75, y = 4.5 C.x = 1.8, y = 19 D.x = 4.5, y = 5.5 Example 2

  15. Concept 2

  16. Use the Third Angles Theorem ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If IJK  IKJ and mIJK = 72, find mJIH. ΔJIK  ΔJIH Congruent Triangles mIJK + mIKJ + mJIK = 180 Triangle Angle-Sum Theorem Example 3

  17. Use the Third Angles Theorem mIJK + mIJK + mJIK = 180 Substitution 72 + 72 + mJIK = 180 Substitution 144 + mJIK = 180 Simplify. mJIK = 36 Subtract 144 from each side. mJIH = 36 Third Angles Theorem Answer:mJIH = 36 Example 3

  18. TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ΔKLM  ΔNJL, KLM  KML,and mKML = 47.5, find mLNJ. A. 85 B. 45 C. 47.5 D. 95 Example 3

  19. Prove That Two Triangles are Congruent Write a two-column proof. Prove:ΔLMNΔPON Example 4

  20. Statements Reasons 1. Given 1. 2. LNM  PNO 2. Vertical Angles Theorem 3. M  O 3. Third Angles Theorem 4. ΔLMNΔPON 4. CPCTC Prove That Two Triangles are Congruent Proof: Example 4

  21. Statements Reasons 1. Given 1. 2. Reflexive Property of Congruence 2. 3.Q  O, NPQ  PNO 3. Given 4. _________________ 4.QNP  ONP ? 5.ΔQNPΔOPN 5. Definition of Congruent Polygons Find the missing information in the following proof. Prove:ΔQNPΔOPN Proof: Example 4

  22. A. CPCTC B. Vertical Angles Theorem C. Third Angles Theorem D. Definition of Congruent Angles Example 4

  23. Concept 3

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