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.

Support Beams

Classify the triangular shape of the support beams in the diagram by its sides and by measuring its angles.

EXAMPLE 2 Classify a triangle in a coordinate plane

SOLUTION

STEP 1 Use the distance formula to find the side lengths.

Classify PQO by its sides. Then determine if the triangle is a right triangle.

OP = y2 – y1( )2x2 – x1( )2 +

= 2 – 0( )2(– 1 ) 0( )2 +– = 5 2.2

OQ = y2 – y1( )2x2 – x1( )2 +

2= – 0( )6 0( )2 +– 3 = 45 6.7

EXAMPLE 2 Classify a triangle in a coordinate plane

PQ = y2 – y1( )2x2 – x1( )2 +

3 – 2( )26( )2 +–= (– 1 ) = 50 7.1

STEP 2 Check for right angles.

The slope of OP is 2 – 0 – 2 – 0

= – 2.

The slope of OQ is 3 – 0 6 – 0

=21 .

1The product of the slopes is – 2

2 = – 1,

so OP OQ and POQ is a right angle.

Therefore, PQO is a right scalene triangle.ANSWER

GUIDED PRACTICE for Examples 1 and 2

1. Draw an obtuse isosceles triangle and an acute scalene triangle.

obtuse isosceles triangle

B

A C

acute scalene triangleP

Q

R

GUIDED PRACTICE for Examples 1 and 2

1. 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.

ABC is a right Isosceles triangle.

ANSWER