5.2—Dilations and Similar Polygons
5.2 Warm Up
1. If ∆QRS  ∆ZYX, identify the pairs of congruent angles
and the pairs of congruent sides.
Solve each proportion.
2.
3.
5.2—Dilations and Similar Polygons
Objective: Identify dilations, similar polygons and triangles.
Scale Factor: the of the lengths of two corresponding sides of
two similar polygons
A dilation with center C and scale factor k is a transformation that maps
𝐶𝑃′
every point P in the plane to a point P’ so that 𝑘 =
(and k ≠ 1)
𝐶𝑃
ratio
A dilation is a reduction if 0 < k < 1
A dilation is an enlargement if k > 1
A dilation is inverted (rotated 180° around the center of dilation),
then dilated if k < 0
The image and the preimage from a dilation are always similar figures.
Examples:
Identify the dilation and find its scale factor.
Similar Polygons: when there is a correspondence between two
polygons such that their corresponding angles are congruent AND
the lengths of corresponding sides are proportional
Theorem: If two polygons are similar, then the ratio of their
perimeters is equal to the ratios of their corresponding side lengths.
Examples:
1. The two polygons are similar. Using the given similarity statement,
list all pairs of congruent angles and write the ratios of the
corresponding sides in a statement of proportionality.
Determine if the polygons are similar. If so, write a similarity
statement and find the scale factor of figure A to figure B. If not
similar, then explain.
1st hour
The polygons are similar. Find the values of the variables.