CHAPTER 4: TRIANGLE RELATIONSHIPS
4.1 Classifying Triangles
Example 1: Classify Triangles by Sides
6
4
6
4
4
5
7
7
4
Example 2: Classify Triangles by Angles and Sides
70˚
5
3
6.4
9
95˚
4
40˚
40˚
70˚
45˚
5.8
Example 3: Identify the Parts of a Triangle
Name the side that is opposite each angle.
a. A
A
b. B
c. C
C
B
4.2 Angle Measures of Triangles
Example 1: Find an Angle Measure
Given mLA= 85˚ and mLB= 43˚, find the mLC.
A
C
B
Example 2: Find Angle Measures
ABC and ABD are right triangles. Suppose
mABD  35
a. Find mDAB.
B
A
b. Find mBCD.
C
D
You Try!
1. Find the mA , if mB  55 and mC  65 .
A
2. Find the mA , if mB  45 and mC  60 .
C
B
3. Find the mA , if mB  22 and mC  68 .
Example 3: Find an Angle Measure.
Given the mA  58 and mC  72, find
m1.
B
A
1
C
4.3 Isosceles and Equilateral Triangles
Example 1: Use the Base Angles Theorem.
Find the mL.
M
L
?
65˚
N
Example 2: Use the Converse of the Base Angles Theorem
Find the value of x, if F  E.
F
12
D
x+3
E
You Try! Find the value of y.
y+7
50˚
9
y˚
Example 3: Find the Side Length of an Equilateral Triangle
Solve for x and determine the length of each side.
R
3x
Q
2x + 10
T
4.4 The Pythagorean Theorem and the Distance Formula
Example 1: Find the Length of the Hypotenuse
Use the Pythagorean Theorem to find c.
c
5
12
Example 2: Find the Length of a Leg
Use the Pythagorean Theorem to find b.
14
b
7
Example 3: Find the Length of a Segment
Find the distance between the points A (2,1) and
B (5,5).
Example 4: Use the Distance Formula
Find the distance between D(1,2) and E(3,-2).
You Try! Find the distance between the following points
A(0,0) and B(3,4)
D(1,4) and E(3,-2)
F(-2,2) and G (-3,-3)
4.5 The Converse of the Pythagorean Theorem
Example 1: Verify a Right Triangle
Is ABC a right triangle?
16
20
12
Example 2: Acute Triangles
Show that the triangle is an acute triangle.
5
√35
4
Example 3: Obtuse Triangles
Show that the triangle is an obtuse triangle.
15
8
12
Example 4: Classifying Triangles
Classify the triangle as acute, right or obtuse.
5
6
8
Example 5: Classifying Triangles
Classify the triangle with the given side lengths as acute, right or obtuse.
a. 4, 6, 7
b. 12, 35, 37
4.6 Medians of a Triangle
Example 1: Draw a Median
In STR, draw a median from S to its opposite
side.
S
4
T
Example 2: Use the Centroid of a Triangle
E is the centroid of ABC and DA = 27. Find EA
and DE.
Example 3: Use the Centroid 2
P is the centroid of QRS and RP = 10. Find the
length of RT
5
6
R
4.7 Triangle Inequalities
Example 1: Order Angle Measures
Name the angles from largest to smallest
V
4
10
T
Example 2: Order Side Length
Name the sides from shortest to longest.
8
U
F
57˚
86˚
D
Example 3: Use the Triangle Inequality
Can the following side lengths form a triangle? Explain.
a. 3, 5, 9
b. 3, 5, 8
37˚
E
c. 3, 5, 7
You Try! Determine whether the following side lengths can form a triangle. Explain how you know.
a. 5, 7, 13
b. 6, 9, 12
c. 10, 15, 25
Q
R
P
T
S