1. Splash Screen

2. Five-Minute Check (over Lesson 4–1) NGSSS Then/Now New Vocabulary
Theorem 4.1: Triangle Angle-Sum Theorem
Proof: Triangle Angle-Sum Theorem
Example 1: Real-World Example: Use the Triangle Angle-Sum Theorem
Theorem 4.2: Exterior Angle Theorem
Proof: Exterior Angle Theorem
Example 2: Real-World Example: Use the Exterior Angle Theorem
Corollaries: Triangle Angle-Sum Corollaries
Example 3: Find Angle Measures in Right Triangles
Lesson Menu

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

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

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

6. A. ΔABC
B. ΔACB
C. ΔADC
D. ΔCAB A B C D
5-Minute Check 4

7. Classify ΔMNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15.
A. scalene
B. isosceles
C. equilateral A B C
5-Minute Check 5

8. Which is not a classification for ΔFGH?
A. acute
B. scalene
C. isosceles
D. equiangular A B C D
5-Minute Check 6

9. Also addresses MA.912.D.6.4 and MA.912.G.8.2.
MA.912.G.2.2 Determine the measures of interior and exterior angles of polygons, justifying the method used.
MA.912.G.8.5 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.
Also addresses MA.912.D.6.4 and MA.912.G.8.2.
NGSSS

10. You classified triangles by their side or angle measures. (Lesson 4–1)
Apply the Triangle Angle-Sum Theorem.
Apply the Exterior Angle Theorem.
Then/Now

11. remote interior angles flow proof
auxiliary line
exterior angle
remote interior angles
flow proof
Vocabulary

12. Concept 1

13. Concept 2

14. 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.
Understand Examine 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.
Example 1

15. Triangle Angle-Sum Theorem
Use the Triangle Angle-Sum Theorem
Plan Find 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
Triangle Angle-Sum Theorem
Simplify.
Subtract 117 from each side.
Example 1

16. 1 and 2 are congruent vertical angles. So, m2 = 63.
Use the Triangle Angle-Sum Theorem
1 and 2 are congruent vertical angles. So, m2 = 63.
Triangle Angle-Sum Theorem
Simplify.
Subtract 142 from each side.
Answer: Therefore, m1 = 63, m2 = 63, and m3 = 38.
Check The sums of the measures of the angles in each triangle should be m = or 180 m2 + m = or 180
Example 1

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

18. Concept 3

19. Concept 4

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

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

22. Concept 5

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

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

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

26. Find m3.
A. 50
B. 45
C. 85
D. 130 A B C D
Example 3

27. End of the Lesson