1. Splash Screen

2. Over Lesson 4–1 5-Minute Check 1 A.acute B.equiangular C.obtuse D.right Classify ΔRST.

3. Over Lesson 4–1 5-Minute Check 1 A.acute B.equiangular C.obtuse D.right Classify ΔRST.

4. Over Lesson 4–1 5-Minute Check 2 A.8 B.10 C.12 D.14 Find y if ΔRST is an isosceles triangle with RS ≅ RT. ___

5. Over Lesson 4–1 5-Minute Check 2 A.8 B.10 C.12 D.14 Find y if ΔRST is an isosceles triangle with RS ≅ RT. ___

6. Over Lesson 4–1 5-Minute Check 3 A.2 B.4 C.6 D.8 Find x if ΔABC is an equilateral triangle.

7. Over Lesson 4–1 5-Minute Check 3 A.2 B.4 C.6 D.8 Find x if ΔABC is an equilateral triangle.

8. Over Lesson 4–1 5-Minute Check 4 A.ΔABC B.ΔACB C.ΔADC D.ΔCAB

9. Over Lesson 4–1 5-Minute Check 4 A.ΔABC B.ΔACB C.ΔADC D.ΔCAB

10. Over Lesson 4–1 5-Minute Check 5 A.scalene B.isosceles C.equilateral Classify ΔMNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15.

11. Over Lesson 4–1 5-Minute Check 5 A.scalene B.isosceles C.equilateral Classify ΔMNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15.

12. Over Lesson 4–1 5-Minute Check 6 A.acute B.scalene C.isosceles D.equiangular Which is not a classification for ΔFGH?

13. Over Lesson 4–1 5-Minute Check 6 A.acute B.scalene C.isosceles D.equiangular Which is not a classification for ΔFGH?

14. CCSS Content Standards G.CO.10 Prove theorems about triangles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others.

15. Then/Now You classified triangles by their side or angle measures. Apply the Triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

16. Vocabulary auxiliary line exterior angle remote interior angles flow proof corollary

17. Concept 1

18. Concept 2

19. Example 1 Use the Triangle Angle-Sum Theorem SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. UnderstandExamine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that  1 and  2 are vertical angles.

20. Example 1 Use the Triangle Angle-Sum Theorem Triangle Angle-Sum Theorem Simplify. Subtract 117 from each side. PlanFind m ∠ 1 first because the measure of two angles of the triangle are known. Use the Vertical Angles Theorem to find m ∠ 2. Then you will have enough information to find the measure of ∠ 3. Solve

21. Example 1 Use the Triangle Angle-Sum Theorem Triangle Angle-Sum Theorem Simplify. Subtract 142 from each side. ∠ 1 and ∠ 2 are congruent vertical angles. So, m ∠ 2 = 63. Answer:

22. Example 1 Use the Triangle Angle-Sum Theorem Triangle Angle-Sum Theorem Simplify. Subtract 142 from each side. Answer: Therefore, m ∠ 1 = 63, m ∠ 2 = 63, and m ∠ 3 = 38. CheckThe sums of the measures of the angles in each triangle should be 180. m ∠ 1 + 43 + 74= 63 + 43 + 74 or 180 m ∠ 2 + m ∠ 3 + 79= 63 + 38 + 79 or 180 ∠ 1 and ∠ 2 are congruent vertical angles. So, m ∠ 2 = 63.

23. Example 1 A.95 B.75 C.57 D.85 Find the measure of ∠ 3.

24. Example 1 A.95 B.75 C.57 D.85 Find the measure of ∠ 3.

25. Concept 3

26. Concept 4

27. Example 2 Use the Exterior Angle Theorem GARDENING Find the measure of ∠ FLW in the fenced flower garden shown. m ∠ LOW + m ∠ OWL = m ∠ FLWExterior Angle Theorem x + 32= 2x – 48Substitution 32= x – 48Subtract x from each side. 80= xAdd 48 to each side. Answer:

28. Example 2 Use the Exterior Angle Theorem GARDENING Find the measure of ∠ FLW in the fenced flower garden shown. m ∠ LOW + m ∠ OWL = m ∠ FLWExterior Angle Theorem x + 32= 2x – 48Substitution 32= x – 48Subtract x from each side. 80= xAdd 48 to each side. Answer: So, m ∠ FLW = 2(80) – 48 or 112.

29. Example 2 A.30 B.40 C.50 D.130 The piece of quilt fabric is in the shape of a right triangle. Find the measure of ∠ ACD.

30. Example 2 A.30 B.40 C.50 D.130 The piece of quilt fabric is in the shape of a right triangle. Find the measure of ∠ ACD.

31. Concept 5

32. Example 3 Find Angle Measures in Right Triangles Find the measure of each numbered angle. If 2 ∠ s form a linear pair, they are supplementary. Exterior Angle Theorem m ∠ 1 = 48 + 56 Simplify. = 104 Substitution 104 + m ∠ 2 = 180 Subtract 104 from each side. 76

33. Example 3 Find Angle Measures in Right Triangles Subtract 132 from each side. 48 Simplify. 132 + m ∠ 4 = 180 Substitution 56 + 76 + m ∠ 4 = 180 Triangle Angle-Sum Theorem (90 – 34) + m ∠ 2 + m ∠ 4 = 180 Simplify. = 42 If 2 ∠ s form a right angle, they are complementary. m ∠ 3 = 90 – 48

34. Example 3 Find Angle Measures in Right Triangles Subtract 131 from each side. 49 Simplify. m ∠ 5 + 143 = 180 Triangle Angle-Sum Theorem m ∠ 5 + 41 + 90 = 180

35. Example 3 Find Angle Measures in Right Triangles Subtract 131 from each side. 49 Simplify. m ∠ 5 + 143 = 180 Triangle Angle-Sum Theorem m ∠ 5 + 41 + 90 = 180 m ∠ 1 = 104, m ∠ 2 = 76, m ∠ 3 = 42, m ∠ 4 = 48, m ∠ 5 = 49

36. Example 3 A.50 B.45 C.85 D.130 Find m ∠ 3.

37. Example 3 A.50 B.45 C.85 D.130 Find m ∠ 3.

38. End of the Lesson