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Intermediate Geometry : How to find if kites are similar

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Example Questions

Example Question #301 : Intermediate Geometry

A kite has two different side lengths of $\displaystyle 4$ and $\displaystyle 12$. Find the measurements for a similar kite.

Possible Answers:

$\displaystyle 6$ and $\displaystyle 36$

$\displaystyle 5$ and $\displaystyle 18$

$\displaystyle 2$ and $\displaystyle 4$

$\displaystyle 8$ and $\displaystyle 24$

$\displaystyle 3$ and $\displaystyle 8$

Correct answer:

$\displaystyle 8$ and $\displaystyle 24$

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 $\displaystyle 4$ and $\displaystyle 12$, they have the ratio of $\displaystyle 4:12=1:3$.

Therefore, find the side lengths that have a ratio of 1:3 $\displaystyle 1:3$.

The only answer choice with this ratio is: $\displaystyle 8:24=1:3$

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Example Question #2 : Kites

A kite has two different side lengths of $\displaystyle 6$ and $\displaystyle 24$. Find the measurements for a similar kite.

Possible Answers:

$\displaystyle 6$ and $\displaystyle 3$

$\displaystyle 2$ and $\displaystyle 5$

$\displaystyle 1$ and $\displaystyle 6$

$\displaystyle 5$ and $\displaystyle 20$

$\displaystyle 7$ and $\displaystyle 30$

Correct answer:

$\displaystyle 5$ and $\displaystyle 20$

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 $\displaystyle 6$ and $\displaystyle 24$, which have the ratio of 1:4 $\displaystyle 1:4$.

The only answer choice with the same relationship between side lengths is: $\displaystyle 5$ and $\displaystyle 20$, which has the ratio of 1:4. $\displaystyle 1:4.$

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Example Question #1 : How To Find If Kites Are Similar

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

Possible Answers:

$\sqrt6:\sqrt{54}$ $\displaystyle \sqrt6:\sqrt{54}$

$\sqrt6:3$ $\displaystyle \sqrt6:3$

$1:\sqrt6$ $\displaystyle 1:\sqrt6$

$\sqrt7:\sqrt6$ $\displaystyle \sqrt7:\sqrt6$

$\sqrt6:1$ $\displaystyle \sqrt6:1$

Correct answer:

$\sqrt6:3$ $\displaystyle \sqrt6:3$

Explanation:

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

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

Rationalize the denominator.

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

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

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Example Question #1 : Kites

Suppose a kite has side lengths of $\displaystyle 4$ and $\displaystyle 5$. What must the side lengths be for a similar kite?

Possible Answers:

6,10 $\displaystyle 6,10$

2,3 $\displaystyle 2,3$

1,2 $\displaystyle 1,2$

12,15 $\displaystyle 12,15$

5,9 $\displaystyle 5,9$

Correct answer:

12,15 $\displaystyle 12,15$

Explanation:

Write the side lengths 4 and 5 as a ratio.

4:5 $\displaystyle 4:5$

The only side lengths that match this ratio by a scale factor of $\displaystyle 3$ is 12:15 $\displaystyle 12:15$.

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

Therefore, the correct side lengths are 12,15 $\displaystyle 12,15$.

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Intermediate Geometry : How to find if kites are similar

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #301 : Intermediate Geometry

Example Question #2 : Kites

Example Question #1 : How To Find If Kites Are Similar

Example Question #1 : Kites

All Intermediate Geometry Resources

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