4.1 Classifying Triangles4.1 Classifying Triangles

ObjectivesObjectives

Identify and classify triangles by anglesIdentify and classify triangles by angles

Identify and classify triangles by sidesIdentify and classify triangles by sides

Parts of a TriangleParts of a Triangle

A A triangletriangle is a 3-sided polygon is a 3-sided polygon The The sidessides of of ∆ABC are ∆ABC are

AB, BC, and ACAB, BC, and AC The The verticesvertices of of ∆ABC are ∆ABC are

A, B, and CA, B, and C Two sides sharing a common Two sides sharing a common

vertex are vertex are adjacent sidesadjacent sides The third side is called the The third side is called the

opposite sideopposite side All sides can be adjacent or All sides can be adjacent or

opposite (it just depends which opposite (it just depends which vertex is being used)vertex is being used)

adjacent

adjacent

Side opposite A

C

A

B

Classifying Triangles by AnglesClassifying Triangles by Angles

ObtuseObtuse1 angle is

obtuse (measure > 90°)

Right1 angle is right(measure = 90°)

One way to classify triangles is by their angles…

AcuteAcuteall 3 angles are

acute (measure < 90°)

An acute ∆ with all angles is an equiangular ∆ .

ARCHITECTURE The triangular truss below is modeled for steel construction. ClassifyJMN, JKO, and OLN as acute, equiangular, obtuse, or right.

Example 1:Example 1:

Answer:JMN has one angle with measure greater than 90, so it is an obtuse triangle.

JKO has one angle with measure equal to 90, so it is a right triangle.

OLN is an acute triangle with all angles congruent, so it is an equiangular triangle.

Example 1:Example 1:

Classifying Triangles by SidesClassifying Triangles by Sides

IsoscelesIsosceles 2 or more

congruent sides

ScaleneScaleneno congruent

sides

Another way to classify triangles is by their sides…

EquilateralEquilateral3 congruent

sides

Answer: UTX and UVX are isosceles.

Identify the isosceles triangles in the figure if

Isosceles triangles have at least two sides congruent.

Example 2a:Example 2a:

Identify the scalene triangles in the figure if

Answer: VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene.

Scalene triangles have no congruent sides.

Example 2b:Example 2b:

Identify the indicated triangles in the figure.

a. isosceles triangles

b. scalene triangles

Answer: ABC, EBC, DEB, DCE, ADC, ABD

Answer: ADE, ABE

Example 2c:Example 2c:

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:Example 3:

Next, substitute to find the length of each side.

Answer: For KLM, and the measure of each side is 7.

Example 3:Example 3:

KL = 7 LM = 7 KM = 7

Answer:

ALGEBRA Find x and the measure of each side of equilateral triangle if and

Your Turn:Your Turn:

COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.

Example 4:Example 4:

Answer: ; since all 3 sides have different lengths, RST is scalene.

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

Example 4:Example 4:

AssignmentAssignment

Geometry:Geometry:Pg. 181 Pg. 181 #13 – 18, 22 – 28, 32, 34#13 – 18, 22 – 28, 32, 34

Pre-AP Geometry:Pre-AP Geometry:

Pg. 181 Pg. 181 #13 – 18, 22 – 29, 32, 34, 36, #13 – 18, 22 – 29, 32, 34, 36, 38 38