1. Over Lesson 10–2 A.A B.B C.C D.D 5-Minute Check 5 A.6.5 ft B.6.6 ft C.6.7 ft D.6.8 ft

2. Splash Screen

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

4. Vocabulary line segment triangle vertex congruent Part of a line containing two endpoints and all the points between them A Figure having three sides The two sides of a triangle (polygon) intersect Line segments that have the same length, or angles that have the same measure, or figures that have the same size and shape

5. Concept A

6. Example 1 Find Angle Measures 100 + 33 + x =180Substitution 133 + x=180Simplify. 133 – 133 + x=180 – 133 Subtract 133 from each side. x=47Simplify. Answer: x is 47, so m  F = 47°. Find the value of x in ΔDEF. Write an equation.

7. A.A B.B C.C D.D Example 1 A.57 B.123 C.139 D.303 Find the value of x in ΔMNO.

8. Example 2 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?

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

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

11. Concept B

12. Example 3 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.

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

14. Concept C

15. Concept D

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

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

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

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

20. End of the Lesson