2. Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Angles of a Triangle Example 1:Find Angle Measures Example 2:Use Ratios to Find Angle Measures Key Concept:Classify Triangles Example 3:Classify Triangles Example 4:Classify Triangles Five-Minute Check

3. Main Idea/Vocabulary Find missing angle measures in triangles. triangle acute triangle right triangle obtuse triangle scalene triangle isosceles triangle equilateral triangle

4. NGSSS MA.8.G.2.3 Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find unknown measure of angles, and the sum of angles in polygons.

5. Key Concept

6. Example 1 Find Angle Measures PARK The city park shown is in the shape of a triangle. Find the value of x. x + 36 + 36= 180 Write the equation. x + 72= 180 Simplify. – 72 – 72 Subtract. x= 108 Simplify. Answer:The value of x is 108°.

7. Example 1 CYP A.39° B.56° C.73° D.146° STONES The paver stone shown below is in the shape of a triangle. Find the value of x.

8. Example 2 The measures of the angles of ΔDEF are in the ratio 1:2:3. What are the measures of the angles? Use Ratios to Find Angle Measures

9. Example 2 Use Ratios to Find Angle Measures x + 2x + 3x= 180 Write the equation. 6x= 180Combine like terms. x= 30 Simplify. Since x = 30, 2x = 2(30) or 60, and 3x = 3(30) or 90. Answer:The measures of the angles are 30°, 60°, and 90°.

10. Example 2 CYP A.18°, 36°, 54° B.18°, 54°, 108° C.15°, 45°, 90° D.30°, 60°, 90° The measures of the angles of ΔQRS are in the ratio 1:3:6. What are the measures of the angles?

11. Key Concept 3

12. Example 3 Classify Triangles Classify the triangle by its angles and by its sides. The triangle has a right angle and no congruent sides. Answer:It is a right scalene triangle.

13. Example 3 CYP A.acute scalene B.acute isosceles C.obtuse scalene D.obtuse isosceles Classify the triangle by its angles and by its sides.

14. Example 4 Classify the triangle by its angles and by its sides. Classify Triangles The triangle has all acute angles and two congruent sides. Answer: It is an acute isosceles triangle.

15. Example 4 CYP A.acute scalene B.acute isosceles C.right scalene D.right isosceles Classify the triangle by its angles and by its sides.

16. A.53° B.80° C.90° D.127° Find the value of x in the triangle. Five Minute Check 1

17. A.15 B.30 C.34 D.71 Find the value of x in the triangle. Five Minute Check 2

18. A.scalene B.isosceles C.equilateral Three sides of a triangle measure 3 centimeters, 4 centimeters, and 5 centimeters. Classify the triangle by its sides. Five Minute Check 3

19. A.acute B.obtuse C.right Two angles of a triangle measure 25° and 45°. Classify the triangle by its angles. Five Minute Check 4

20. A.Yes; if all three angles of a triangle are congruent, then all three sides are congruent, and the triangle is equilateral. B.No; you do not know the lengths of the sides. All three angles of a triangle measure 60°. Can you classify the triangle by its sides? Explain. Five Minute Check 5

21. A.equilateral B.scalene C.acute D.right Which of the following triangles could NOT be classified as isosceles? Five Minute Check 6