Glencoe Math: Course 3, Volume 2
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Glencoe Math: Course 3, Volume 2 View details
4. Properties of Similar Polygons
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Exercise 14 Page 551

What transformation maps a figure onto another if they do not have the same size?

Example Transformation Sequence: Translation followed by dilation
Missing Side Measure: x=16.25

Practice makes perfect

We are given two similar polygons and want to determine the transformations that map one figure onto the other. Then we want to find the missing side measure.

We will do these things one at a time.

Transformations

Since the figures are similar, they have the same shape but they do not have the same size. Let's determine what transformations map one onto the other.

similar polygons

A translation followed by a dilation maps the first quadrilateral onto the second.

Missing Side Measure

Because the figures are similar, the ratio of the corresponding side measures is constant. Therefore, to find the missing side measure we will set up a proportion. 26/x=12/7.5 Let's solve the equation! Our first step in solving is to remove the denominators from both sides of the equation using the Multiplication Property of Equality.

26/x=12/7.5
â–¼
Simplify
26/x * x=12/7.5 * x
26 = 12/7.5 * x
26 = 12x/7.5
26 * 7.5 = 12x/7.5 * 7.5
195 = 12x/7.5 * 7.5
195 = 12x
12x=195

Finally, we can isolate x using the Division Property of Equality.

12x=195
â–¼
Solve for x
12x/12=195/12
12 * x/12=195/12
12/12 * x=195/12
1 * x=195/12
x=195/12
x=16.25