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Dorchester-02-04-2025-Similar Triangles Assessment

Total questions: 23

Worksheet time: 6hrs 45mins

Name
Class
Date
1.

Triangles EFG and RST are similar. FG:ST = 3:12, and RS = 156, what is the length of EF?

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2.

Triangles JKL and PQR are similar. The length of the sides of JKL are 5x - 155, x + 47, and x + 71. The perimeter of JKL is 306. The length of the longest side of PQR is 151 + x, what is the perimeter of PQR?

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3.

Triangles HIJ and OPQ are similar. The length of the sides of HIJ are 79x - 6, 76 + 2x, and 154 + x. The perimeter of HIJ is 388. The length of the smallest side of OPQ is 190 + 5x, what is the length of the longest side of OPQ?

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4.

Triangles FGH and OPQ are similar. FH:OQ = 7:11, and OP = 385, what is the length of FG?

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5.

A tree 37 1/2 feet tall casts a shadow 80 feet long. Brad is 3 3/4 feet tall. How long is Brad's shadow?

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6.

In right ABC, is the altitude to hypotenuse . If DB = 7 and AD = 8, find CD.

a)

15

b)


1 171\ \frac{1}{7}

c)

2142\sqrt[]{14}

d)

15\sqrt[]{15}

e)

1

7.

Mary claims that the triangles below are similar by angle-angle (AA). Do you agree or disagree with Mary?

a)

Agree, because there are two pairs of congruent angles.

b)

Disagree, because we can't determine if the sides are proportional.

c)

Disagree, because the two given angles are not congruent.

d)

Agree, because the triangles look similar.

8.

Is triangle ABC similar to triangle DEF?

a)

No, because the corresponding sides are not proportional.

b)

No, because we don't know if the included angles are congruent.

c)

Yes, by SSS

d)

Yes, by SAS

9.

Josh claims that these triangles are similar by SSS. Do you agree or disagree with Josh?

a)

Agree, because the triangles have a pair of congruent sides.

b)

Agree, because all of the ratios for the corresponding sides are equal.

c)

Disagree, because we cannot determine similarity without knowing the angle measures.

d)

Disagree, because all of the ratios for the corresponding sides are not equal.

10.

Conclude whether triangle BEN is similar to triangle MAT.

a)

Yes, by SAS

b)

Yes, by AAA

c)

Yes, by AA

d)

Yes, by SSS

11.

Determine if triangle VEZ is similar to triangle MAG.

a)

No, because all of the angles are not congruent.

b)

Yes, by AA

c)

Yes, by SAS

d)

No, because the sides are not proportional.

12.

Triangle LMN ~ Triangle (a)   ​

Choose from the below words
PQN
QPN
NPQ
NQP
13.
To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown.  What is AB to the nearest meter?
14.

Given the following triangles ARE SIMILAR. Label the missing measurements.

15.

The triangles given are similar.

Solve for x. 

16.

Which proportion should you use to find x?

a)

15 / x = 7 / 14

b)

x / 7 = 14 / 15

c)

7 / x = 15 / 14

d)

x / 15 = 7 / 14

17.

If △XYZ ∼ △ABC and XY = 6, XZ = 8, and AB = 9, what is the length of AC?

(a)  

18.

These are ​ (a)   triangles because they have the ​ (b)   shape but ​ (c)   size. The sides are ​ (d)   .

Choose from the below words
similar
congruent
same
different
proportional
19.

Two triangles have sides in proportion, but no angles are given. The ​ ​ (a)   theorem determines their similarity.

Choose from the below words
SSS Similarity
AA Similarity
SAS Similarity
None of the above
20.

Two triangles are ​ (a)   because they have (b)   shapes but (c)   sizes. Their corresponding sides are ​​ (d)   .

Choose from the below words
Similar
Same
Different
Proportional
Equal
Congruent
21.

Match the given triangle properties with the correct similarity theorem:

a)

Two triangles have two sides proportional, and the included angle is congruent.

1.

SAS Similarity

b)

Two triangles have three sets of proportional sides but no given angles.

2.

SSS Similarity

c)

Two triangles have two corresponding angles congruent.

3.

AA Similarity

d)

Two triangles have three congruent sides but different orientations.

4.

Not Similar

22.

Match each problem scenario with the correct similarity theorem or concept:

a)

A ladder leans against a wall, forming two right triangles with the ground. The angle between the ladder and the ground is the same in both cases.

1.

AA Similarity

b)

A model airplane is built to be exactly 1/50th the size of a real airplane, with all corresponding measurements proportional.

2.

Scale Factor

c)

A computer-generated image of a triangle is resized using a scale factor of 1.5, increasing all side lengths proportionally while maintaining the same angle measures.

3.

Dilation

d)

Two triangles are confirmed to be similar because their sides are in a ratio of 2:3, but the angles have not been verified.

4.

SSS Similarity

e)

A triangle is given where two sides of one triangle are proportional to two sides of another, and the included angles are congruent.

5.

SAS Similarity

23.

On the coordinate plane, the vertices

of △ABC are A(0,0), B(4,0), and C(2,6).

The vertices of △DEF are D(0,0), E(8,0), and F(4,12).

Are the two triangles similar?

Draw and label the axis.

Plot and label the points on the

coordinate plane.

Be sure to write which similarity theorem is used, if any.

Write all your work on the grid NEATLY and ORDERLY!