DETERMINE WHETHER THE PAIR OF FIGURES IS SIMILAR WORKSHEET

Problem 1 :

A 20 cm wide picture frame surrounds a painting which is 100 cm by 60 cm. Are the two rectangles shown here similar?

Solution

Give brief reasons why these figures possess similar triangles:

Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

At 4 pm one day the shadow of a pine tree was 5 m long. At the same time a 2 m long broom handle had a shadow which was 3 m long. How high is the pine tree?

Solution

After establishing similarity, find the unknowns in:

Problem 6 :

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Problem 7 :

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Problem 8 :

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Problem 9 :

The Mexican flag is 63 inches long and 36 inches high. Is the drawing at below similar to the Mexican flag ?

Solution

Problem 10 :

A student’s rectangular desk is 30 inches long and 18 inches wide. The teacher’s rectangular desk is 60 inches long and 36 inches wide. Are the desks similar?

Solution

Problem 11 :

The two triangles are similar. Find the measure of the angle

a) ∠B      b)  ∠L   c)  ∠J

Solution

Problem 12 :

Given △FGH ∼ △QRT, name the corresponding angles and the corresponding sides.

Solution

Problem 13 :

You want to buy only photos that are similar rectangles. Which of the photo sizes should you buy ?

4 in × 5 in

5 in × 7 in

8 in × 12 in

11 in × 14 in

Solution

Problem 14 :

Are the following figures always, sometimes, or never similar? Explain.

a. Two triangles

b. Two squares

c. Two rectangles

d. A square and a triangle

Solution

Problem 15 :

Can you draw two quadrilaterals each having two 130° angles and two 50° angles that are not similar? Justify your answer.

Solution

Problem 16 :

All of the angle measures in the sign are 90°.

a. Each side length is increased by 20%. Is the new sign similar to the original?

b. Each side length is increased by 6 inches. Is the new sign similar to the original?

Solution

Find x given that the figures are similar :

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

A town plans to build a new swimming pool. An Olympic pool is rectangular with a length of 50 meters and a width of 25 meters. The new pool will be similar in shape to an Olympic pool but will have a length of 40 meters. Find the perimeters of an Olympic pool and the new pool

Solution

Problem 8 :

In the diagram, △ABC ∼ △DEF. Find the area of △DEF.

Solution

Problem 9 :

A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of an NCAA court and of the new court in the school.

Solution

Problem 10 :

Describe and correct the error in finding the area of rectangle B. The rectangles are similar.

Solution

Problem 11 :

In the following the two polygons are similar. Find the values of x and y.

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Problem 12 :

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Problem 13 :

In table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table.

Solution