Classify angles and triangles 10.3 Ray- Extend in one direction Line- Extends in two directions Angles- Two rays have the same endpoint Vertex-The common endpoint Sides- the two rays that make up the angle The symbol means angle You can classify angles four ways Use the vertex and a point <ABC or <CBA Use the vertex only <B Use a number <1 Classify angles and triangles 10.3

Name the angle below in two ways Name the angle below in two ways. Then classify it as acute, right, obtuse, or straight. A. JKL, K; acute B. LKJ, K; right C. JKL, K; obtuse D. LKJ, J; obtuse

Classify Angles A. Matching F. B. C. D. E. 1. Acute ____ 2. Right ____ 3. Obtuse ____ 4. Straight ____ 5. Vertical ____ 6. Congruent ____ A B

Key Concept 3

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

Example 4 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.

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

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 + 36 + 36 = 180 Write the equation. x + 72 = 180 – 72 – 72 x = 108 Answer: The value of x is 108°.

Example 1 CYP 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°

Example 2 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?

Example 2 Use Ratios to Find Angle Measures x + 2x + 3x = 180 Write the equation. 6x = 180 Combine 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 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°