EXAMPLE 1

1. Support Beams Classify the triangular shape of the support beams in the diagram by its sides and by measuring its angles. EXAMPLE 1 Classify triangles by sides and by angles SOLUTION The triangle has a pair of congruent sides, so it is isosceles. By measuring, the angles are 55° , 55° , and 70° . It is an acute isosceles triangle.

2. Classify PQOby its sides. Then determine if the triangle is a right triangle. Use the distance formula to find the side lengths. STEP1 2 2 – – ( ( ) ) OP = + + 2 2 – – ( ( ) ) y x x y y y x x 2 1 2 2 2 1 1 1 2 2 ( – ( ) (– 1 ) ) 0 2 – 0 2.2 + = = 5 OQ = 2 2 ( – ( ) 6 ) 0 – 0 3 6.7 + = = 45 EXAMPLE 2 Classify a triangle in a coordinate plane SOLUTION

3. PQ = 2 2 ( – ) 6 (– 1 ) ) 3 – ( 2 7.1 + = = Check for right angles. STEP2 The slope ofOPis 2 – 0 3 – 0 1 . – 2. The slope ofOQis = = – 2 – 0 2 6 – 0 1 – 2 The product of the slopes is – 1 , = 2 – ( ) 2 + 2 – ( ) so OPOQand POQ is a right angle. y x x y 2 2 1 1 50 ANSWER Therefore, PQOis a right scalene triangle. EXAMPLE 2 Classify a triangle in a coordinate plane

4. Draw an obtuse isosceles triangle and an acute scalene triangle. B A C Q obtuse isosceles triangle R P acute scalene triangle for Examples 1 and 2 GUIDED PRACTICE

5. Triangle ABChas the vertices A(0, 0), B(3, 3), and C(–3, 3). Classify it by its sides. Then determine if it is a right triangle. ANSWER ABCis a right Isosceles triangle. for Examples 1 and 2 GUIDED PRACTICE