How to find if kites are similar

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Geometry › How to find if kites are similar

Questions 1 - 4

1

Suppose the ratio of a kite's side lengths is $\sqrt 2$ to $\sqrt3$ . Find a similar kite.

$\sqrt6:3$

$\sqrt6:1$

$1:\sqrt6$

$\sqrt7:\sqrt6$

$\sqrt6:\sqrt{54}$

Explanation

To find a similar kite, first take the ratios of the two sides and convert this to fractional form.

$\sqrt2:\sqrt3= \frac{\sqrt2}{\sqrt3}$

Rationalize the denominator.

$\frac{\sqrt2}{\sqrt3}=\frac{\sqrt2}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}=\frac{\sqrt6}{3}$

The ratios of $\sqrt2:\sqrt3$ matches that of $\sqrt6:3$ .

2

Suppose a kite has side lengths of and . What must the side lengths be for a similar kite?

Explanation

Write the side lengths 4 and 5 as a ratio.

The only side lengths that match this ratio by a scale factor of is .

$4\cdot 3:5\cdot 3 \rightarrow 12:15$

Therefore, the correct side lengths are .

3

A kite has two different side lengths of and . Find the measurements for a similar kite.

and

and

and

and

and

Explanation

A kite is a geometric shape that has two sets of equivalent adjacent sides. In order for two kites to be similar their sides must have the same ratios.

Since, the given kite has side lengths and , they have the ratio of .

Therefore, find the side lengths that have a ratio of .

The only answer choice with this ratio is:

4

A kite has two different side lengths of and . Find the measurements for a similar kite.

and

and

and

and

and

Explanation

A kite is a geometric shape that has two sets of equivalent adjacent sides. In order for two kites to be similar their sides must have the same ratios.

The given side lengths for the kite are and , which have the ratio of .

The only answer choice with the same relationship between side lengths is: and , which has the ratio of

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