4.1 Classifying Triangles

Objectives

 Identify and classify triangles by angles  Identify and classify triangles by sides

Classifying Triangles by Angles

67 ° One way to classify triangles is by their angles… 142 ° 13 ° 37 ° 76 °

Acute

all 3 angles are acute (measure < 90 ° ) 25 °

Obtuse

1 angle is obtuse (measure > 90 °) 42 ° 48 ° 90 °

Right

1 angle is right (measure = 90 °)

An acute ∆ with all angles



is an

equiangular ∆

.

Classifying Triangles by Sides

Another way to classify triangles is by their sides…

Equilateral

3 congruent sides

Isosceles

2 congruent sides

Scalene

no congruent sides

Example 3: ALGEBRA

Find d and the measure of each side of equilateral triangle KLM if and Since 

KLM

is equilateral, each side has the same length. So 5 =

d

Example 3:

Next, substitute to find the length of each side. KL = 5+2 KL = 7

LM =12-5 LM = 7 KM = 4(5)-13 KM = 7

Answer:

For 

KLM,

each side is 7. and the measure of

Example 4: COORDINATE GEOMETRY Find the measures of the sides of

 RST. Classify the triangle by sides. RS (-1,-3), (4, 4) ST (4,4), (8, -1) RT (8, -1), (-1,-3)

Example 4:

Use the distance formula to find the lengths of each side.

distance  (

x

2 

x

1 ) 2  (

y

2 

y

1 ) 2

RS

 ( 4  (  1 ) 2  (  4  (  3 )) 2

ST

 ( 8  4 ) 2  (  1  4 ) 2

RT

 (  1  8 ) 2  (  3  (  1 ) 2

Answer:

; since all 3 sides have different lengths, 

RST

is scalene.