1. Similarity and Ratios Investigation 4
Which cats appear to be similar?
Equivalent ratios between adjacent side lengths in figures
can also be used to prove similarity.
Ratio Comparison of two quantities.
Equivalent Ratios Ratio’s whose fraction representations are equal.
Adjacent Next to each other.

2. 4.1 Ratios within Similar Parallelograms
Base on equivalent adjacent side ratios, which figures below are similar?
4 cm B
2 cm
8 cm C A
4 cm
8 cm
3 cm
Figure
Long Side
Short Side
Ratio A 8 4
8 = 2 B 3
8 = 2.6 C 2
4 = 2
Figures
A and C have equivalent adjacent side ratios: therefore, they are SIMILAR!

3. 4.2 Ratios within Similar Triangles
25° B
25° A
3 in.
3.25 in.
2.5 in.
2 in.
4 in.
136° C
3 in.
56°
94°
19°
1.5 in.
Triangle
Corresponding Angles
Adjacent Sides Ratio
(longest/shortest) A
25°, 19°, 136° = 3 B =
1.5 C
56°, 94°, 30°
= 2
Triangles
A and B have equivalent adjacent side ratios and congruent angles: therefore, they are SIMILAR!

4. 4.2 Ratios within Similar Triangles
RECAP
How can Similarity be proven?
Parallelogram
Scale factor
Adjacent side ratios
Triangle
Corresponding angle measures
(If corresponding angle measures are also equal.)

5. 4.3 Finding Missing Parts Using Similarity to Find Measurements
When you know two figures are similar,
you can find missing lengths in two ways:
Scale factor from
one figure to the other.
Find scale factor
4 = 2 2
2 cm
4 cm
3 cm
Multiply or Divide by scale factor
2 x 2 = 4 cm x = 6 cm
3 x 2 = 6 cm
Smaller to bigger multiply scale factor
Bigger to smaller divide by scale factor x

6. 2) Ratios of the side lengths within each figure.
4.3 Finding Missing Parts
2) Ratios of the side lengths within each figure.
Set up adjacent side ratios
6.5 = 3.25 x
6.5 in.
3 in.
4 in.
Find equivalent fractions
6.5 ÷ 2 = 3.25
3 ÷ 2 = x
3 = x = 1.5 cm 2
3.25 in. x
2 in.