IDENTIFY THE SHAPES ARE SIMILAR CONGRUENT OR NEITHER WORKSHEET

Tell whether the shapes are similar, congruent or neither.

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 :

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Problem 8 :

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Problem 9 :

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Problem 10 :

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Problem 11 :

In the diagram, ABGH ≅ CDEF.

1. Identify all pairs of congruent corresponding parts.

2. Find the value of x.

3. In the diagram at the left, show that △PTS ≅ △RTQ.

Solution

Problem 12 :

a) Find m∠DCN.

b) What additional information is needed to conclude that △NDC ≅ △NSR?

Solution

Problem 13 :

△XYZ ≅ △MNL. Copy and complete the statement.

a) m∠M = ______

b) m∠Z = ______

c) XY =

d) m∠Y = ______

Solution

Problem 14 :

Find the values of x and y. ABCD ≅ EFGH

Solution

Problem 1 :

Two angles are congruent if they have:

(a) Same name     b) Equal measures

(c) Unequal measures  (d) None of these

Solution

Problem 2 :

If a ∆ ABC ≅ ∆ PQR, then AB is equal to:

(a) QR   (b) PQ    (c) PR     (d) None of these

Solution

Problem 3 :

In ∆ ABC and ∆PQR, AB = 4 cm, BC = 5 cm, AC = 6 cm and PQ = 4 cm, QR = 5 cm, PR = 6 cm, then which of the following is true:

(a) ∆ ABC ≅ ∆ QRP     (b) ∆ ABC ≅ ∆ PQR

(c) ∆ ABC ≅ ∆ PRQ     (d) ∆ ABC ≅ ∆ QPR

Solution

Complete the similarity statement for the similar figures and then find the scale factor. Write proportions and solve for missing side lengths.

Problem 4 :

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Problem 5 :

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Problem 6 :

Use the given information to write and solve a system of linear equations to find the values of x and y.

a)  △LMN ≅ △PQR, m∠L = 40°, m∠M = 90°, m∠P = (17x − y)°, m∠R = (2x + 4y)°

b) △STU ≅ △XYZ, m∠T = 28°, m∠U = (4x + y)°, m∠X = 130°, m∠Y = (8x − 6y)

Solution

Problem 7 :

In the diagram, ABEF ≅ CDEF.

a. Explain how you know that BE ≅ DE and ∠ABE ≅ ∠CDE.

b. Explain how you know that ∠GBE ≅ ∠GDE.

c. Explain how you know that ∠GEB ≅ ∠GED.

d. Do you have enough information to prove that △BEG ≅ △DEG? Explain.

Solution

Problem 1 :

Lance and Alien is 5 feet tall. His shadow is 8 feet long.

At the same time of day, a tree's shadow is 32 feet long. What is the height of the tree ?

Solution

Problem 2 :

Pentagon JKLMN is similar to pentagon VWXYZ, what is the measurement of angle X ?

Solution

Problem 3 :

Triangle PQR is similar to triangle DEF as shown.

which describes the relationship between the corresponding sides of the two triangles ?

a)  PQ/DE = 4/6        b)  PQ/DE = 6/4

c)  PQ/EF = 4/9        d)  PR/DE = 6/6

Solution

Problem 4 :

A six foot tall person is standing next to flag pole. The person is casting a shadow 1 1/2 feet in length while a flagpole is casting a shadow 5 feet in length. How tall is the flagpole ?

a)  30 ft     b) 25 ft    c)  20 ft     d)  15 ft

Solution

Problem 5 :

The angle of the roof on Kaya's doll house is 56°. She built a scale model of the doll house with a scale ratio of 1 : 4, what is the measure of the angle of the roof of the model ?

a) 14°     b) 34°    c) 56°    d)  224°

Solution

Problem 6 :

In triangle PQR is similar to XYZ.

What is the perimeter of XYZ ?

a) 21 cm     b) 63 cm    c) 105 cm    d)  126 cm

Solution

Problem 7 :

If the triangles ADE and ABC shown in the figure below are similar, what is the value of x ?

a) 4     b) 5    c) 6    d)  8     e)  10

Solution

Problem 8 :

In the figure given below, the two triangles are similar. What is the value of x ?

a) 12.4     b) 13.2    c) 14    d)  18.6     e)  22.1

Solution

Problem 9 :

Mr. Smith is having some photos enlarged for studio. He wants to enlarge a photo that is 5 inches by 7 inches so the dimensions are 3 times larger than the original. How many times larger than the original photo will the area of the new photo be ?

a) 3     b) 6    c) 9    d)  30

Solution

Problem 10 :

During a total eclipse of the Sun, the moon is directly in line with the Sun and blocks the Sun’s rays. The distance DA between Earth and the Sun is 93,000,000 miles, the distance DE between Earth and the moon is 240,000 miles, and the radius AB of the Sun is 432,500 miles. Use the diagram and the given measurements to estimate the radius EC of the moon.

Solution