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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Similar Polygons

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Exercise 20 Page 556

The ratio between corresponding sides are the same for all pairs of corresponding sides in similar polygons.

2

Practice makes perfect

We are told that the polygons are similar, and we want to find the value of x.

Since the figures are similar, their corresponding sides are also similar. Let's identify corresponding sides.

There is only one side on each polygon included between two indicated right angles. These are corresponding sides.
Similarly, there is only one side on each polygon included opposite to the previously described side. Thus, they are also corresponding sides.
There are also PR and ZV, which are also corresponding sides.
The remaining sides are also corresponding.

The ratio between corresponding sides is the same for all pairs of corresponding sides. 8x-1/12 = 3x-1/4 Let's solve this ratio for x.

8x-1/12=3x-1/4

▼

Solve for x

LHS * 12=RHS* 12

8x-1/12 * 12=3x-1/4 * 12

FracMultDenomToNumber

a/12* 12 = a

8x-1=3x-1/4 * 12

MoveRightFacToNum

a/c* b = a* b/c

8x-1=(3x-1)12/4

a/b=.a /4./.b /4.

8x-1=(3x-1)3

Distribute 3

8x-1=9x-3

LHS+3=RHS+3

8x+2=9x

LHS-8x=RHS-8x

2=x

Rearrange equation

x=2

Subchapter links

Exercises p.554-559