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Splash Screen. Five-Minute Check (over Chapter 4) Then/Now New Vocabulary Theorems: Perpendicular Bisectors Example 1: Use the Perpendicular Bisector Theorems Theorem 5.3: Circumcenter Theorem Proof: Circumcenter Theorem Example 2: Real-World Example: Use the Circumcenter Theorem

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 4) Then/Now New Vocabulary Theorems: Perpendicular Bisectors Example 1: Use the Perpendicular Bisector Theorems Theorem 5.3: Circumcenter Theorem Proof: Circumcenter Theorem Example 2: Real-World Example: Use the Circumcenter Theorem Theorems: Angle Bisectors Example 3: Use the Angle Bisector Theorems Theorem 5.6: Incenter Theorem Example 4: Use the Incenter Theorem Lesson Menu

  3. A B C Classify the triangle. A. scalene B. isosceles C. equilateral 5-Minute Check 1

  4. A B C D Find x if mA = 10x + 15, mB = 8x – 18, andmC = 12x + 3. A. 3.75 B. 6 C. 12 D. 16.5 5-Minute Check 2

  5. A B C Name the corresponding congruent sides if ΔRST ΔUVW. A. R  V,S  W,T  U B. R  W,S  U,T  V C. R  U,S  V,T  W D. R  U,S  W,T  V 5-Minute Check 3

  6. A B C A. B. C. D. , Name the corresponding congruent sides if ΔLMN ΔOPQ. 5-Minute Check 4

  7. A B C D Find y if ΔDEF is an equilateral triangle and mF = 8y + 4. A. 22 B. 10.75 C. 7 D. 4.5 5-Minute Check 5

  8. You used segment and angle bisectors. (Lesson 1–3 and 1–4) • Identify and use perpendicular bisectors in triangles. • Identify and use angle bisectors in triangles. Then/Now

  9. perpendicular bisector Vocabulary

  10. Concept

  11. Use the Perpendicular Bisector Theorems A. Find the measure of BC. BC = AC Perpendicular Bisector Theorem BC = 8.5 Substitution Answer: 8.5 Example 1

  12. Use the Perpendicular Bisector Theorems B. Find the measure of XY. Answer: 6 Example 1

  13. Use the Perpendicular Bisector Theorems C. Find the measure of PQ. PQ = RQ Perpendicular Bisector Theorem 3x + 1 = 5x – 3 Substitution 1 = 2x – 3 Subtract 3x from each side. 4 = 2x Add 3 to each side. 2 = x Divide each side by 2. So, PQ = 3(2) + 1 = 7. Answer: 7 Example 1

  14. A B C D A. Find the measure of NO. A. 4.6 B. 9.2 C. 18.4 D. 36.8 Example 1

  15. A B C D B. Find the measure of TU. A. 2 B. 4 C. 8 D. 16 Example 1

  16. A B C D C. Find the measure of EH. A. 8 B. 12 C. 16 D. 20 Example 1

  17. Concept

  18. Use the Angle Bisector Theorems A. Find DB. DB = DC Angle Bisector Theorem DB = 5 Substitution Answer:DB = 5 Example 3

  19. Use the Angle Bisector Theorems B. FindWYZ. Example 3

  20. Use the Angle Bisector Theorems WYZ  XYZ Definition of angle bisector mWYZ = mXYZ Definition of congruent angles mWYZ = 28 Substitution Answer:mWYZ = 28 Example 3

  21. Use the Angle Bisector Theorems C. Find QS. QS = SR Angle Bisector Theorem 4x – 1 = 3x + 2 Substitution x – 1 = 2 Subtract 3x from each side. x = 3 Add 1 to each side. Answer: So, QS = 4(3) – 1 or 11. Example 3

  22. A B C D A. Find the measure of SR. A. 22 B. 5.5 C. 11 D. 2.25 Example 3

  23. A B C D B. Find the measure of HFI. A. 28 B. 30 C. 15 D. 30 Example 3

  24. A B C D C. Find the measure of UV. A. 7 B. 14 C. 19 D. 25 Example 3

  25. Splash Screen

  26. median • altitude Vocabulary

  27. Altitude:(of a triangle) is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. Median:(of a triangle) is a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side.

  28. Concept

  29. End of the Lesson

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