1. Five-Minute Check (over Lesson 3) Mathematical Practices 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

2. What is coordinate of the image of the point (3, –4) after a reflection in the y-axis?
B. (–3, –4)
C. (3, 4)
D. (4, 3)
5-Minute Check 1

3. CD has endpoints C(–1, 6) and D(3, 4)
CD has endpoints C(–1, 6) and D(3, 4). What are the coordinates of the image of point C after a rotation of 90° about the origin?
A. C’(–6, –1)
B. C’(1, –6)
C. C’(6, –1)
D. C’(6, 1)
5-Minute Check 1

4. This figure does not line symmetry.
State whether the figure appears to have line symmetry. If so, how many lines of symmetry does it have?
A. yes; 8 lines
B. yes; 4 lines
yes; 2 lines
This figure does not line symmetry.
5-Minute Check 2

5. The figure has rotational symmetry
The figure has rotational symmetry. State the order and magnitude of symmetry.
A. 8; 60°
B. 8; 45°
C. 10; 45°
D. 10; 36°
5-Minute Check 4

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

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

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

9. Concept 1

10. Concept 2

11. 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

12. 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

13. 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

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

15. Concept 3

16. Concept 4

17. 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

18. 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
Example 2

19. Concept 5

20. 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.
= 70
If 2 s form a linear pair, they are supplementary.
Substitution
70 + m2 = 180
Subtract 70 from each side.
110
Example 3

21. Exterior Angle Theorem m∠3 + 64 = m∠2
Find Angle Measures in Right Triangles
Exterior Angle Theorem
m∠ = m∠2
Substitution
m∠ = 110
Subtract 64 from each side.
m∠3 = 46
Exterior Angle Theorem
m∠ = m∠3 + 32
Substitution
m∠ =
Simplify.
m∠ = 78
m∠5 = 37
Subtract 41 from each side.
Example 3

22. Triangle Angle-Sum Theorem m∠4 + m∠5 + 41 = 180
Find Angle Measures in Right Triangles
Triangle Angle-Sum Theorem
m∠4 + m∠ = 180
Substitution
m∠ = 180
Simplify.
m∠ = 180
Subtract 132 from each side.
102
m1 = 70, m2 = 110, m3 = 46, m4 = 102, m5 = 37
Example 3

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