4.1 Types of Triangles You can classify a triangle by its sides and its angles. There are THREE different classifications for triangles based on their sides. There are FOUR different classifications for triangles based on their angles.

EQUILATERAL – 3 congruent sides ISOSCELES – at least two sides congruent SCALENE – no sides congruent Triangles By Sides

Triangles by Angles EQUIANGULAR – all angles are congruent ACUTE – all angles are acute RIGHT – one right angle OBTUSE – one obtuse angle

Scalene Triangles No sides are the same length

Isosceles Triangles At least two sides are the same length

Acute Triangles Acute triangles have three acute angles

Right Triangles Right triangles have one right angle

Obtuse Triangles Obtuse triangles have one obtuse angle

Classify this triangle. Right Scalene

Classify this triangle. Obtuse Isosceles

Classify this triangle. Acute Scalene

Classify this triangle. Acute Isosceles

Classify this triangle. Obtuse Scalene

Classify this triangle. Right Isosceles

GUIDED PRACTICE for Examples 1 and 2 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. ABC is a right Isosceles triangle. ANSWER

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= y 2 –y 1 ( ) 2 x 2 –x 1 ( ) 2 + = 2–0 ( ) 2 (– 1 ) 0 ( ) 2 + – = OQ= y 2 –y 1 ( ) 2 x 2 –x 1 ( ) = –0 ( )6 0 ( ) 2 + – 3 =

EXAMPLE 2 Classify a triangle in a coordinate plane PQ= y 2 –y 1 ( ) 2 x 2 –x 1 ( ) 2 + 3– 2( ) 2 6 ( ) 2 + – = (– 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 = The 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

Classifying Triangles 4.2 Triangles