Similar Polygons

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Similar Polygons
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Informal Definition of Similar Figures

• Two figures are similar if they have the same
  shape.
• (They do not necessarily have the same size.)

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Formal Definition of Similar Polygons

• Two polygons are similar iff their corresponding
  angles are congruent,and
• (lengths of) corresponding sides are proportional.

1. ? A ? ? D
2. ? B ? ? E
3. ? C ? ? F

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Proportional

• (Lengths of) sides are proportional iff ratios of
  (lengths of) corresponding sides are equal.
• For example
• so the sides are
• proportional.

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Scale Factor

• The ratio of corresponding sides of
• similar polygons.
• Example The scale factor
• from ?ABC to ?_____
• is____.
• from ?ZYX to ?ABC
• is____.

ZYX
2
1/2
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Naming Similar Polygons
Must match the corresponding letters
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Applying the Definition - Angles
Must match the corresponding vertices
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Applying the Definition - Sides
Must match the corresponding sides
Proportional means all of the ratios are equal!
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Example 1
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Example 1
Given Find AC
Step 1 Write out a proportion of for the sides.
(Be sure to match up corresponding letters!)
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Example 1
Given Find the lengths of the missing sides.
Step 2 Replace the sides with the lengths from
the problem.
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Example 1
Given Find the lengths of the missing sides.
Step 3 Cross-multiply and solve.
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Example 1
Given
You should be able to find CD and BD as well!
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Example 2
Given Find the scale factor of ABDC to RPSQ
Remember the scale factor is same as the ratio of
the sides. Always put the first polygon mentioned
in the numerator.
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Example 3
ABCD ? EFGH. Solve for x, y and z.
Step 1 Write a proportion using names of
sides. Step 2 Substitute values. Step 3
Cross-multiply to solve. Step 4 Repeat to find
other values.
y 10
z 15
x 7.5
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Dilations and Scale Factor

• A dilation is a transformation that changes the
  size of an object.
• The scale factor is the ratio of the lengths of
  the corresponding sides of two similar polygons.
  It indicates the relative size of one polygon
  compared the another.

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Congruent Triangles

• Are congruent triangles similar?
• What is the scale factor between two congruent
  triangles?