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Similarity, Dilations, Right Triangle Assessment

Last updated about 5 years ago

25 questions

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Question 1

1.

What is the value of n?

n=3

n=4

Question 2

2.

Line segment MN has its endpoints at M(4, 8) and N(−8, 2). If line segment MN is dilated by a scale factor of 2 about the center of dilation (4,4), what would be the coordinates of M′and N′’?

M' (8, 16) and N′(−16,4)

M' (2, 4) and N′(−4,1)

M' (4, 12) and N′(−20,0)

M' (12, 20) and N′(−12,8)

Question 3

3.

8

3

6

1

Question 4

4.

No. The corresponding angles are not congruent

No. The lengths of the sides are not given

Yes. The triangles are both scalene

Yes. The obtuse angles for both triangles are equal

Question 5

5.

Triangle ABC is similar to triangle DEF with the side lengths of triangle ABC being 5 times the side lengths of triangle DEF.
What characteristic of the two triangles is the same?

the angles

the perimeters

the areas

the side lengths

Question 6

6.

Triangle PQR is translated 3 units right and dilated by a scale factor of 5 about the origin to form triangle XYZ. Which statement is true?

△PQR is congruent to △XYZ because a translation and a dilation both preserve angles of the triangle.

△PQR is similar to △XYZ because a translation and a dilation both preserve side lengths of the triangle.

△PQR is congruent to △XYZ because a translation and a dilation both preserve side lengths of the triangle.

△PQR is similar to △XYZ because a translation and a dilation both preserve angles of the triangle.

Question 7

7.

△EFG is dilated by a scale factor of 15 with a center of dilation at (2,2) to form new △XYZ. Which statement is true?

△EFG≅△XYZ​ because the side lengths of the triangle are preserved after dilation.

△EFG∼△XYZ​ because the side lengths of the triangle are preserved after dilation.

​△EFG≅△XYZ​ because the angles of the triangle are preserved after dilation.

△EFG∼△XYZ​ because the angles of the triangle are preserved after dilation.

Question 8

8.

Question 9

9.

Two triangle have two pairs of corresponding congruent angles. Which statement about the triangles is true?

The triangles must be congruent

The triangles must be right triangles

The triangles must be similar

The triangles must be acute triangles

Question 10

10.

Question 11

11.

Question 12

12.

△RST is similar to △LMN by AA criteria.

△RST is similar to △LNM by AA criteria.

△RST is congruent to △LMN by AA criteria.

△RST is congruent to △LNM by AA criteria.

Question 13

13.

The length of one leg of an isosceles right triangle is 2 units. What is the length of the hypotenuse?

4 units

2 units

Question 14

14.

Question 15

15.

Consider triangle PQR with line segment ST parallel to line segment QR.

The table shows a proof that line segment ST, parallel to line segment QR, divides the sides of the triangle proportionally.

Which are the correct reasons for Step 3 and Step 5?

Reason 3: Alternate interior angles are equal.
Reason 5: Corresponding sides of similar triangles are equal.

Reason 3: Corresponding angles are equal.
Reason 5: Corresponding sides of similar triangles are proportional.

Reason 3: Alternate interior angles are equal.
Reason 5: Corresponding sides of similar triangles are proportional.

Reason 3: Corresponding angles are equal.
Reason 5: Corresponding sides of similar triangles are equal.

Question 16

16.

Question 17

17.

25 units

31.2 units

12 units

21.4 units

Question 18

18.

Question 19

19.

51 units

52 units

47 units

48 units

Question 20

20.

The area of the larger sail will be 4 times the area of the smaller sail

The area of the larger sail will be 8 times the area of the smaller sail

The area of the larger sail will be 16 times the area of the smaller sail

the area of the larger sail will be 32 times the area of the smaller sail

Question 21

21.

Question 22

22.

AB=4; JK=8

AB=2; JK=8

AB=8; JK=4

AB=8; JK=2

Question 23

23.

6 cm

9 cm

8 cm

12 cm

Question 24

24.

Which statements are true?
Select ALL that apply

Question 25

25.

13 units

27 units

8 units

6 units