4.1 Classifying Triangles. Objectives Identify and classify triangles by angles Identify and...
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Transcript of 4.1 Classifying Triangles. Objectives Identify and classify triangles by angles Identify and...
4.1 Classifying Triangles
Objectives
Identify and classify triangles by angles
Identify and classify triangles by sides
Parts of a Triangle
A triangle is a 3-sided polygon The sides of ∆ABC are
AB, BC, and AC The vertices of ∆ABC are
A, B, and C Two sides sharing a common
vertex are adjacent sides The third side is called the
opposite side All sides can be adjacent or
opposite (it just depends which vertex is being used)
adjacent
adjacent
Side opposite A
C
A
B
Classifying Triangles by Angles
Obtuse1 angle is
obtuse (measure > 90°)
Right1 angle is right(measure = 90°)
One way to classify triangles is by their angles…
Acuteall 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:
60° 60°
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 cont:
Classifying Triangles by Sides
Isosceles 2 congruent
sides
Scaleneno congruent
sides
Another way to classify triangles is by their sides…
Equilateral3 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 2:
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 3:
Identify the indicated triangles in the figure.
a. isosceles triangles
b. scalene triangles
Answer: ABC, EBC, DEB, DCE, ADC, ABD
Answer: ADE, ABE
Example 4:
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 5:
Next, substitute to find the length of each side.
Answer: For KLM, and the measure of each side is 7.
Example 5 cont:
KL = 7 LM = 7 KM = 7
Answer:
ALGEBRA Find x and the measure of each side of equilateral triangle if and
Example 6:
COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.
Example 7:
Answer: ; since all 3 sides have different lengths, RST is scalene.
Use the distance formula to find the lengths of each side.
Example 7 cont:
Assignment
Geometry:Pg. 180 #5 - 10, 13-18, 32 - 37