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Chapter 4 – Scale Factors and
Similarity Key Terms
• Corresponding Angles – Angles that have the same
relative position in two geometric figures
• Corresponding Sides – Sides that have the same relative
position in two geometric figures
• Similar – have the same shape but different size and have
equal corresponding angles and proportional corresponding
sides.
4.3 Similar Triangles
Learning Outcome: To be able to
identify similar triangles and
determine if they are proportional
Symbols
Δ triangle
° degrees
~ similar
angle
Identify Similar Triangles
Example 1:
Determine if ∆ABC is similar to ∆EFG.
B
12
A
F
9
4
E
3
G
C
Similar triangles have corresponding angles that are equal
in measure and corresponding sides that are proportional
in length.
Identify Similar Triangles
Note:
B is the same as
ABC
Example 1:
Determine if ∆ABC is similar to ∆EFG.
3
Corresponding Angles
are proportional with a
scale factor of equal.
Compare Corresponding Angles
∠𝐴 = 90° 𝑎𝑛𝑑 ∠𝐸 = 90°
∠𝐵 = 37° 𝑎𝑛𝑑∠𝐹 = 37°
∠𝐶 = 53° 𝑎𝑛𝑑∠𝐺 = 53°
Side Question:
What does the
sum of all the
angles of a
triangle ALWAYS
add up to?
Compare Corresponding Sides
The
𝐴𝐵 12
corresponding
=
=3
sides are
𝐸𝐹
4
𝐵𝐶 15
proportional
=
=3
𝐹𝐺
5
with a scale
𝐴𝐶 9
factor of 3.
= =3
𝐸𝐺
3
∆ABC is ~ ∆EFG
Show you Know – Determine if each
pair of triangles is similar.
Assignment
• Page 150 (4-7,9,10,12-14
PERIOD 1
BRING FOOD FOR THE MINGA FOOD BANK
COLLECTION TOMORROW!!!
4.3 Similar Triangles
Learning Outcome: To be able to solve
problems involving similar triangles and
find missing side lengths
Use Similar Triangles to Determine a
Missing Side Length
Example 2: Kyle is drawing
triangles for a math
puzzle. Use your
knowledge of similar
triangles to determine
a) If the triangles are
L
similar
b) the missing side length
K
21
T
M
10.5
U
7
8
V
Example 2 a) If the triangles are similar
Check that ΔKLM is similar to ΔTUV.
The sum of the angles in a
triangle are 180°.
K = 180° - 50°-85°
= 45°
U = 180° - 85°-45°
= 45°
L
Compare corresponding Angles:
K
Note: It is not
necessary to
prove both
conditions for
similarity. One
is sufficient.
T
M
1
U
All pairs of corresponding angles are equal.
Therefore, ΔKLM ~ ΔTUV
7
8
V
Example 2 b) the missing side length
You can compare corresponding sides to determine the scale
K
factor.
3
L
The scale factor is 3. You can solve for the
unknown length.
T
M
1
U
7
8
V
Example 2 b) the missing side length
Method 1: Use a scale factor
K
3
x=31.5
L
The missing side length is 31.5 units.
T
M
1
U
7
8
V
Example 2 b) the missing side length
Method 1: Use a Proportion
Since the triangles are similar, you can use equal
K
ratios to set up a proportion.
x1.5
L
T
M
1
x1.5
7
x=31.5
The missing side length is 31.5 units.
U
8
V
Similar Triangles
• Similar triangles have been multiplied by a scale
factor with enlargement or reduction.
Consequently, similar triangles have:
• Corresponding Angles - Equal internal angles
• Corresponding Sides - Proportional side lengths
(because of scale factor)
• Unlike polygons in general, to check if triangles
are similar, checking one of the conditions above
suffices. If one is true, the other follows.
Show you Know – Solve using a
method of your choice
Assignment
• Page 150 (9-14)
• Due Tuesday, October 23rd
Assignment
• Page 150 (1-2, 5, 7-9, 13-14)
• Due Friday, October 18th