Basic Geometry : How to find if rectangles are similar

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #411 : Plane Geometry

Rectangles 1

Figure NOT drawn to scale

Refer to the above figure.

True or false: Rectangle  Rectangle .

Possible Answers:

False

True 

Correct answer:

False

Explanation:

Two rectangles are similar if and only if their sides are in proportion. Specifically, 

Rectangle  Rectangle 

if 

Since  is located at the point , it follows that  and . Since  is located at the point , it follows that  and . Substituting in the aforementioned proportion statement, we get

.

Reducing to lowest terms, this is

.

This is false, so Rectangle  Rectangle .

Example Question #11 : Quadrilaterals

Congruent rectangle

Consider the similar rectangles  and  shown here. The lengths of the following sides are given:

What is the length of the side ?

Possible Answers:

Correct answer:

Explanation:

Comparing the sides  and , we see that is  the length of , as shown here:

.

Since these two rectangles are similar, all pairs of corresponding sides are similar. Hence, the ratio of  to  is also , and we can calculate the length of  by setting up and solving a proportion:

.

Hence, the length of the side  is  units.

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