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7.4 Similar Triangles
Today I will learn how to use the properties
of similar triangles to solve problems.
Corresponding Sides
• Triangles are similar if their corresponding
(matching) angles are equal and the ratio of their
corresponding sides are in proportion.
c
a’
c’
a
b’
b
a b c
 
a' b' c'
The ratio of the sides of one triangle are equal
to the ratio of the sides on the second triangle
Language of Triangles
A
• Hatch Marks: Demonstrate equal length
B
• Isosceles Triangle: A triangle with two equal length sides/angles
• Naming an Angle: Three capital letters with middle letter being the
vertex of the angle (E.g. LABD = 30o)
• Perpendicular Bisector: A line segment that passes at 90 degrees
half way along another line segment
• Sum of Interior Angles of Triangle: Add to 180 degrees
C
D
Example 1

Ex 1) Identify the similar triangles in the following diagrams.
Equal angles are marked on the diagrams.
DOG~TAC
RUN~GUM
PAT~MAG
Example 2

A person who is 2.2 m tall has a shadow that is 1.8 m long. At the same time,
a flagpole has a shadow that is 9 m long. Determine the height of the
flagpole to the nearest tenth of a metre. Hint: draw a diagram.
Let x represent the length of the height
of the flagpole in meters
𝑥
9
=
2.2 1.8
1.8𝑥 = 19.8
𝑥 = 11
The flagpole is 11 meters tall
x
2.2m
9m
1.8m
Example 3

A surveyor wants to determine the width of a river. She measures
distances and angles on land and sketches this diagram.
What is the width of the river, PQ?
PQR~STR
𝑄𝑅 𝑃𝑄
=
𝑇𝑅 𝑆𝑇
(12)
𝑃𝑄
=
(15) (20)
240 = 15𝑃𝑄
𝑃𝑄 = 16
The river is 16 meters wide.
Example 4

Determine the length of XY in each pair of similar triangles.
XYZ~PQR
𝑋𝑌 6
=
8
4
4𝑋𝑌 = 48
𝑋𝑌 = 12𝑐𝑚
XYV~WZV
𝑋𝑌 5.0 + 4.5
=
2.5
5
𝑋𝑌 9.5
=
2.5
5
5𝑋𝑌 = 23.75
𝑋𝑌 = 4.75𝑐𝑚