Download Similarity and Proportion Notes

Math 3 Honors
Name: ________________________
Similarity and Proportion Notes
Example 1:
x  3 14

4
7
7(x+3) = 4(14)
7x + 21 = 56
7x = 35
x=5
3 12

x 8
2
6
x
2(1) = 6x
2 = 6x
2/6 =x = 1/3
Example 2:
3(8) = 12x
24 = 12x
x=2
7
x

4: Solve for x:
12 36
5: Solve for y:
Example 3:
8
12

y2 9
2z 2
8
6: Solve for z:
9
SIMILAR SHAPES: If two shapes are similar, then the ratio of their corresponding sides are equal
18
z
x
21
10
y
6
20
15
27
x
9
18
y
8
z
x = _____ y = ____ z = ______
x = ____
y = ______, z = ________
16
15
y
12
x
z
10
14
x = ___________,
y = ______________,
z = _________________
25
x+5
10
X
4
35
Find x = ____________
11
17
34
Y
y = _________________
Find x = __________________
y+7
18
27
30
x – 12
V
9
25
2x + 3
42
129.5
147
18
5y – 2
Find x = _____________
Find x = _____________
y = _____________
y = _____________
v = _____________
Scale Factor of
Sides
Scale factor of
Perimeter
Scale factor of Area
Scale factor of
Volume
a:b
a:b
a2:b2
a3:b3
2:7
4:25
1:8
1:3
85% of the
original
Example 5: Two triangles are similar. The length of corresponding sides are 3:5.
The perimeter of the smaller triangle is 12cm. What is the perimeter of the larger triangle?
The area of the larger triangle is 100cm2. What is the area of the of the smaller triangle?
Example 10: Two triangles are similar. The triangles have areas of 36cm2 and 25cm2.
Two sides of the larger triangle is 12 cm and 18cm. The side of the smaller triangle that isn’t
corresponding to the two given sides of the larger triangle is 5cm. Find the missing sides and
the perimeter of the triangles
Methods for Proving Triangles Similar:
1. Angle-Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to two ________________________ of another
triangle, then the triangles are ___________________________.
2. Side-Side-Side (SSS) Similarity Theorem
If the lengths of the corresponding sides of two triangles are ________________________, then
the triangles are similar.
3. Side-Angle-Side (SAS) Similarity Theorem
If an angle of one triangle is _________________________________ to an angle of another
triangle and the sides that include these angles are _________________________________,
then the triangles are similar.
What is the distance across the river?
Using Similar Triangles:
How tall is the building?