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McGraw Hill Glencoe Algebra 2, 2012

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McGraw Hill Glencoe Algebra 2, 2012 View details

7. Congruent and Similar Figures

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Exercise 7 Page P21

In similar figures, the ratio between corresponding sides is always the same.

x=8, y=21

Practice makes perfect

We are told that the polygons are similar, and want to find the values of x and y for the missing side lengths. Consider the given diagram.

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

There is only one side on each polygon included between two acute angles. These are corresponding sides.
Similarly, there is only one side on each polygon included between two obtuse angles. Therefore, they are also corresponding sides.
The sides included between an acute and an obtuse angle are also corresponding.

We can visualize the above information in the diagram.

In similar figures, the ratio between corresponding sides is always the same. Let's write the ratios that we can see in our diagram. 6/9=x/12=14/y We can use the ratio without variables to solve for the values of x and y. Let's solve for x first.

6/9= x/12

▼

Solve for x

a/b=.a /3./.b /3.

2/3=x/12

LHS * 12=RHS* 12

2/3(12)=x

MoveRightFacToNum

a/c* b = a* b/c

2(12)/3=x

Multiply

24/3=x

Calculate quotient

8=x

Rearrange equation

x=8

We will solve for y in a similar way.

6/9= 14/y

▼

Solve for y

a/b=.a /3./.b /3.

2/3=14/y

Cross multiply

2(y)=3(14)

Multiply

2y=42

.LHS /2.=.RHS /2.

y=21

Subchapter links

Exercises p.21-P21