Honors Geometry Unit 4.1
By: Destiny Moon and Katja Ziemer
TRIANGLES CAN BE CLASSIFIED TWO DIFFERENT WAYS
1. By side lengths
2. By angle measures
1.Classifying triangles by side lengths
Scalene: no congruent sides
Isosceles: at least 2 sides are congruent
Equilateral: all sides are congruent
2. Classifying triangles by angle measures
Acute: all angles are acute
Equiangular: all angles are acute and congruent (each angle is 60
degrees)
Obtuse: one obtuse, and two acute angles
Right: one right angle, two acute angles (add up to 90 degrees)
Sample Problems:
Triangle DES is an equilateral triangle with DE= x+3, ES=3x-3, and
SD= 2x. Find the length of each side.
2x = x+3
-x
-x
x=3
D
DE= x+3
3+3
6
ES= 3x-3
3(3)-3
9-3
6
SD=2x
2(3)
6
E
3x-3
S
Sample Problems:
Triangle KAT is an isosceles triangle, with KA=4x+2, AT=5x, and
TK=3+1. The base is line segment TK. Find the length of each side.
5x = 4x+2
-4x
-4x
x=2
KA= 4x+2
4(2)+2
8+2
10
A
AT= 5x
5(2)
10
TK= 3x+1
3(2)+1
6+1
7
K
3x+1
T
Sample Problems:
Triangle ABC is an equiangular with <ABC= 4x, <BCA= 3x+15, and <CAB= x+45.
Find the measure of each angle.
4x = 3x+15
-3x -3x
x = 15
B
<ABC= 4x
4(15)
60
<BCA= 3x+15
3(15)+15
45+15
60
<CAB= x+45
15+45
60
*Short cut: if a triangle is
equiangular,
then all angles are 60 degrees
4x
x+45
A
3x+15
C
Classify Triangle
Classify each triangle by the number of congruent sides or congruent
segments.Answers are on the next slide.
5.
6.
1.
3.
2.
4.
Classify Triangle
Classify each triangle by the number of congruent sides or congruent
segments.
5.Obtuse
6.Equiangular
1.Equilateral
3.Isosceles
2.Right
4.Scalene
Practice Problems:
Find the measure of the sides of triangle MON and classify by its side lengths.
M(-2,2), O(1,0), N(-3,-4)
Go to the next side to see the answer and the work.
Practice Problems:
Distance Formula: √(x1-x2)2+(y1-y2)2
This is used to calculate the length of
each side.
Find the measure of the sides of triangle MON and classify by its side lengths.
M(-2,2), O(1,0), N(-3,-4)
MO= √(-2-1)2+(2-0)2
√-32+22
√9+4
√13
ON=√(1- -3)2+(0- -4)2
√(1+3)2+(0+4)2
√42+42
√16+16
√32
√16·2
√16√2
4√2
NM=√(-3- -2)2+(-4-2)2
√(-3+2)2+(-4-2)2
√-12-62
√1+36
√37
Since none of the sides of the triangle are the congruent, or the same length, we
know that the triangle should be classified as an isosceles triangle.
Practice Problems:
Triangle MET is an equilateral triangle,ME=3x-12, ET=4y+100,
Find the value of x and y, and the measure of side MT.
Go to the next side to see the answer and the work.
MT=5x+4y.
Practice Problems:
Triangle MET is an equilateral triangle,ME=3x-12, ET=4y+100,
MT=5x+4y
3x-12=4y+100
+12
+12
3x=4y+112
-4y
-4y
3x-4y=112
(Equation #1)
5x+4y=3x-12
-3x
-3x
2x+4y=12
(Equation #2)
2x+4y=-12
3x-4y=112
(Cancel out y)
5x=100
÷5
÷5
X=20
2x+4y=-12
2(20)+4y=-12
(Plug in the
answer for x)
40+4y=-12
-40
-40
4y=-52
÷4
÷4
y=-13
MT=5x+4y
MT=5(20)+4(-13)
(Plug in x and y values)
MT=100-52
MT=48
Practice Problems:
Triangle LMN is an isosceles triangle with base LN. <LMN = 12x and
<MLN = x+20. Find the measures of all of the angles.
Go to the next side to see the answer and the work.
Practice Problems:
Triangle LMN is an isosceles triangle with base LN. <LMN = 12x and
<MLN = x+20. Find the measures of all of the angles.
12x+2(x+20) = 180
12x+2x+40 = 180
14x+40 =180
-40
-40
14x = 140
x = 10
<LMN = 12x
12(10)
120
<MLN = x+20
10+20
30
<MNL = 30
*If a triangle is isosceles, then the
base angles are congruent.
Work Cited
Mr. Pricci’s math packet (Honors Geometry Congruent Triangles)