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

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

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.

Key Concept

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

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.

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

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°.

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?

Key Concept 3

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.

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.

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.

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.

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

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

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

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

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

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