Unit 1 - Similar Figures and Proportions
Similar Figures have the same shape, but not necessarily the same size.
1) Figures are Similar if:
**Corresponding angles are congruent (the angles have the same measurement).
**Corresponding sides are proportional.
Proportion: An equation which states that two ratios (or two fractions) are equal.
Example:
2
8
3 = 12
YES!
5
15
7 = 21
YES!
6
12
9 = 27
NO!
How to Solve Proportions with a Variable:
3
x
4 = 8
2
5
x = 15
4x = 24
4 4
5x = 30
5
5
x=6
x=6
Cross
multiply
2) Similar figures are related by scale factors (tells you how much the figure is enlarged or reduced)
3) If the scale factor of a dilation is greater than 1, the image will be bigger (enlarged),
if the scale factor is less than 1, the image will be smaller (reduced), and if the scale
factor is = 1, the image will be the same (congruent) as the original figure.
**Examples of Similar Figures:
**Examples of Congruent Figures:
Congruent Figures :
1) Congruent figures have the same size and shape.
2) Congruent figures are similar.
3) Their corresponding angles are congruent and their corresponding sides are congruent.