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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 • Find missing angle measures in triangles. • triangle • scalene triangle • acute triangle • isosceles triangle • right triangle • equilateral triangle • obtuse triangle 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. Find Angle Measures PARK The city park shown is in the shape of a triangle. Find the value of x. x + 36 + 36 = 180 x + 72 = 180 – 72 – 72 x = 108 Write the equation. Simplify. Subtract. Simplify. Answer: The value of x is 108°. STONES The paver stone shown below is in the shape of a triangle. Find the value of x. A. 39° B. 56° C. 73° D. 146° Use Ratios to Find Angle Measures 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 x + 2x + 3x = 180 6x = 180 x = 30 Write the equation. Combine like terms. 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°. The measures of the angles of ΔQRS are in the ratio 1:3:6. What are the measures of the angles? A. 18°, 36°, 54° B. 18°, 54°, 108° C. 15°, 45°, 90° D. 30°, 60°, 90° 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. Classify the triangle by its angles and by its sides. A. acute scalene B. acute isosceles C. obtuse scalene D. obtuse isosceles Classify Triangles Classify the triangle by its angles and by its sides. The triangle has all acute angles and two congruent sides. Answer: It is an acute isosceles triangle. Classify the triangle by its angles and by its sides. A. acute scalene B. acute isosceles C. right scalene D. right isosceles Find the value of x in the triangle. A. 53° B. 80° C. 90° D. 127° Find the value of x in the triangle. A. 15 B. 30 C. 34 D. 71 Three sides of a triangle measure 3 centimeters, 4 centimeters, and 5 centimeters. Classify the triangle by its sides. A. scalene B. isosceles C. equilateral Two angles of a triangle measure 25° and 45°. Classify the triangle by its angles. A. acute B. obtuse C. right All three angles of a triangle measure 60°. Can you classify the triangle by its sides? Explain. 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. Which of the following triangles could NOT be classified as isosceles? A. equilateral B. scalene C. acute D. right