1. Splash Screen

2. Five-Minute Check (over Lesson 10–2) Then/Now New Vocabulary
Key Concept: Angles of a Triangle
Example 1: Find Angle Measures
Example 2: Use Ratios to Find Angle Measures
Key Concept: Types of Angles
Example 3: Real-World Example: Classify Angles
Key Concept: Classify Triangles by Angles
Key Concept: Classify Triangles by Sides
Example 4: Classify Triangles
Lesson Menu

3. Name all the sets of numbers to which 0.54 belongs?__
A. rational
B. whole
C. irrational
D. rational, integer
5-Minute Check 1

4. A. >
B. <
C. ≥
D. =
5-Minute Check 2

5. Which list of numbers is correctly ordered from least to greatest?
5-Minute Check 3

6. Solve y2 = 12. Round to the nearest tenth if necessary.
B. 6
C. –3.5, 3.5
D. 3.5
5-Minute Check 4

7. A. 6.5 ft
B. 6.6 ft
C. 6.7 ft
D. 6.8 ft
5-Minute Check 5

8. Which of the following is an example of an irrational number?D.
5-Minute Check 6

9. You solved equations by adding or subtracting. (Lesson 4–3)
Find the missing angle measure of a triangle.
Classify triangles by properties and attributes.
Then/Now

10. line segment
triangle
vertex
congruent
Vocabulary

11. Concept A

12. Find the value of x in ΔDEF.
Find Angle Measures
Find the value of x in ΔDEF.
Write an equation.
x = 180 Substitution
133 + x = 180 Simplify.
133 – x = 180 – Subtract 133 from each side.
x = 47 Simplify.
Answer: x is 47, so mF = 47°.
Example 1

13. Find the value of x in ΔMNO.
B. 123
C. 139
D. 303
Example 1

14. Use Ratios to Find Angle Measures
ALGEBRA The measures of the angles of a triangle are in the ratio 2:3:5. What are the measures of the angles?
Example 2

15. 2x + 3x + 5x = 180 Write the equation.
Use Ratios to Find Angle Measures
2x + 3x + 5x = 180 Write the equation.
10x = 180 Combine like terms.
Divide each side by 10.
x = 18 Simplify.
Since x = 18, 2x = 2(18) or 36, 3x = 3(18) or 54, and 5x = 5(18) or 90.
Answer: The measures of the angles are 36°, 54°, and 90°.
Example 2

16. ALGEBRA The measures of the angles of a certain triangle are in the ratio 3:5:7. What are the measures of the angles?
A. 12°, 60°, 84°
B. 30°, 50°, 70°
C. 36°, 60°, 84°
D. 40°, 60°, 80°
Example 2

17. Concept B

18. Answer: 45° is less than 90°, so it is an acute angle.
Classify Angles
HUMAN JAWS Humans have jaws that can open to about 45°. What type of angle is formed by the jaws of a human?
Answer: 45° is less than 90°, so it is an acute angle.
Example 3

19. A bird’s beak can open to about 80°. What kind of angle is this?
A. acute
B. right
C. obtuse
D. straight
Example 3

20. Concept C

21. Concept D

22. A. Classify the triangle below by its angles and by its sides.
Classify Triangles
A. Classify the triangle below by its angles and by its sides.
Angles: The triangle has an obtuse angle.
Sides: The triangle has no congruent sides.
Answer: The triangle is an obtuse scalene triangle.
Example 4

23. B. Classify the triangle by its angles and by its sides.
Classify Triangles
B. Classify the triangle by its angles and by its sides.
Angles: The triangle has a right angle.
Sides: The triangle has two congruent sides.
Answer: The triangle is a right isosceles triangle.
Example 4

24. A. Classify the triangle by its angles and by its sides.
A. right scalene
B. obtuse scalene
C. obtuse isoceles
D. acute equilateral
Example 4 CYP A

25. B. Classify the triangle by its angles and by its sides.
A. right isoceles
B. obtuse isoceles
C. obtuse scalene
D. acute equilateral
Example 4 CYP B

26. End of the Lesson