Transcript Similarity and Ratios Investigation 4

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.
4.1 Ratios within Similar
Parallelograms
8 cm
4 cm
Based on equivalent adjacent side ratios, which figures below are similar?
A
B
C
2 cm
4 cm
8 cm
3 cm
Figure
Long Side
Short Side
Ratio
A
8
4
8
4
= 2
B
8
3
8
3
= 2.6
C
4
2
4
2
= 2
Figures
A and C have
equivalent adjacent
side ratios: therefore,
they are SIMILAR!
4.2 Ratios within Similar
Triangles
6.5 in.
25°
A
136°
25°
B
2 in.
19°
Triangle
Corresponding
Angles
Adjacent Sides
Ratio
(longest/shortest)
A
25°, 19°, 136°
6.5
3
= 2.16
B
25°, 19°, 136°
3.25 = 2.16
1.5
C
56°, 94°, 30°
3
1.5
= 2
2.5 in.
C
56° 94°
1.5 in.
Triangles
A and B have
equivalent
adjacent side
ratios and
congruent
angles:
therefore, they
are SIMILAR!
4.2 Ratios within Similar Triangles
How can Similarity be proven?
Parallelogram
• Scale factor
• Adjacent side ratios
Triangle
• Scale factor
• Corresponding angle measures
• Adjacent side ratios
(If corresponding angle measures are also equal.)
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:
1)Scale factor from
one figure to the other.
2 cm
4 cm
•Find scale factor
4 =2
2
3 cm
•Multiply or Divide by scale factor
x
2 x 2 = 4 cm
x = 6 cm
3 x 2 = 6 cm
Smaller to bigger multiply scale factor
Bigger to smaller multiply by the inverse
4.3 Finding Missing Parts
2) Ratios of the side
lengths within each
figure.
6.5 = 3.25
3
6.5 in.
3 in.
•Set up adjacent side ratios
4 in.
x
•Find equivalent fractions
6.5 ÷ 2 = 3.25
3
3.25 in.
x
2 in.
÷ 2 =
3 = 1.5
2
x
x = 1.5 cm