How to find if parallelograms are similar

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Geometry › How to find if parallelograms are similar

Questions 1 - 4

1

A parallelogram has adjacent sides with the lengths of and . Find a pair of possible adjacent side lengths for a similar parallelogram.

and

and

and

and

Explanation

Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.

The solution is:

$6:9=(6\div3):(9\div 3)=2:3$

, (divide both numbers by the common divisor of ).

2

A parallelogram has adjacent sides with the lengths of and . Find a pair of possible adjacent side lengths for a similar parallelogram.

and

and

and

and

Explanation

Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.

The ratio of the first parallelogram is:

Applying this ratio we are able to find the lengths of a similar parallelogram.

$4:13=(4\times 3):(13\times3 )=12:39$

3

A parallelogram has adjacent sides with the lengths of and . Find a pair of possible adjacent side lengths for a similar parallelogram.

Explanation

Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.

The ratio of the first parallelogram is:

$15:5\rightarrow 3:1$

Applying this ratio we are able to find the lengths of the second parallelogram.

$15:5=(15\div 5):(5\div 5)=3:1$

4

A parallelogram has adjacent sides with the lengths of and . Find a pair of possible adjacent side lengths for a similar parallelogram.

Explanation

Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.

The ratio of the first parallelogram is:

$28:8 \rightarrow 28\div4:8\div4 \rightarrow 7:2$

Thus by simplifying the ratio we can see the lengths of the similar triangle.

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