EXAMPLE 1 Classify triangles by sides and by

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

EXAMPLE 2 Classify a triangle in a coordinate plane Classify PQO by its sides. Then determine if the triangle is a right triangle. SOLUTION STEP 1 Use the distance formula to find the side lengths. OP = = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 ( (– 1 ) – 0 ) 2 + ( 2 – 0 ) 2 = OQ = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 = ( 6 – 0 )2 + ( 3 – 0 )2 = 5 2. 2 45 6. 7

EXAMPLE 2 Classify a triangle in a coordinate plane PQ = = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 ( 6 – (– 1 )) 2 + ( 3 – 2 ) 2 = 50 7. 1 STEP 2 Check for right angles. 2– 0 The slope of OP is = – 2– 0 The slope of OQ is 3 – 0 = 1. 2 6– 0 1 The product of the slopes is – 2 = – 1, 2 so OP OQ and ANSWER Therefore, POQ is a right angle. PQO is a right scalene triangle.

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

GUIDED PRACTICE 2. for Examples 1 and 2 Triangle ABC has 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. SOLUTION STEP 1 Use the distance formula to find the side lengths. AB = = BC = = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 (( 3 ) – 0 )2 + ( 3 – 0 )2 = ( x 2 18 4. 2 = 400 20 x 1 ) 2 + ( y 2 – y 1 ) 2 ( – 3) 2 + ( 3 – 3 ) 2

GUIDED PRACTICE AC = = for Examples 1 and 2 ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 ( (– 3 – 0 ) ) 2 + ( 3 – 0 ) 2 = 18 4. 2 STEP 2 Check for right angles. The slope of AB is 3 – 0 = 1. 3– 0 The slope of AC is 3 – 0 = – 1. – 3– 0 The product of the slopes is 1(– 1) = – 1 , so AB AC and ANSWER Therefore, BAC is a right angle. ABC is a right Isosceles triangle.