Similarity, Dilations, Right Triangle Assessment

Last updated over 5 years ago

25 questions

1

G.SRT.A.1

1

G.SRT.A.1

1

G.SRT.A.1

1

G.SRT.A.2

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G.SRT.A.2

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G.SRT.A.2

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G.SRT.A.2

1

G.SRT.A.3

1

G.SRT.A.3

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G.SRT.A.3

1

G.SRT.A.3

1

G.SRT.A.3

1

G.SRT.B.4

1

G.SRT.B.4

1

G.SRT.B.4

1

G.SRT.B.4

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G.SRT.B.4

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G.SRT.B.5

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G.SRT.B.5

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G.SRT.B.5

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G.SRT.B.5

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G.SRT.B.5

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G.SRT.B.4

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G.SRT.B.5

1

G.SRT.B.5

What is the value of n?

n=3

n=4

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)

8

3

6

1

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

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

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.

△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.

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

△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.

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

4 units

2 units

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.

25 units

31.2 units

12 units

21.4 units

51 units

52 units

47 units

48 units

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

AB=4; JK=8

AB=2; JK=8

AB=8; JK=4

AB=8; JK=2

6 cm

9 cm

8 cm

12 cm

Which statements are true?
Select ALL that apply

13 units

27 units

8 units

6 units

What is the value of n?

n=3

n=4

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)

8

3

6

1

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

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

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.

△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.

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

△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.

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

4 units

2 units

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.

25 units

31.2 units

12 units

21.4 units

51 units

52 units

47 units

48 units

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

AB=4; JK=8

AB=2; JK=8

AB=8; JK=4

AB=8; JK=2

6 cm

9 cm

8 cm

12 cm

Which statements are true?
Select ALL that apply

13 units

27 units

8 units

6 units

Similarity, Dilations, Right Triangle Assessment

Similarity, Dilations, Right Triangle Assessment

What is the value of n?

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′’?

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?

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?

△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?

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

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

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?

Which statements are true?Select ALL that apply

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?

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?

Which statements are true?
Select ALL that apply