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Section 8.1 and 8.2: Similarity

Total questions: 9

Worksheet time: 15mins

Name
Class
Date
1.

Find the scale factor from DEFG to PQRS.

a)

2/3

b)

3/2

c)

3

d)

1/3

2.

List all pairs of congruent angles.

a)

∠D = ∠R

∠E = ∠S

∠G = ∠Q

∠F = ∠P

b)

∠D = ∠G

∠E = ∠F

∠R = ∠S

∠Q = ∠P

c)

∠D = ∠P

∠E = ∠Q

∠F = ∠R

∠G = ∠S

d)

∠D = ∠S

∠G = ∠P

∠E = ∠R

∠F = ∠Q

3.

Write the ratios of the corresponding side lengths as a statement of proportionality.

a)

PQDE=QREF=RSFG=SPGD\frac{\text{PQ}}{DE}=\frac{QR}{EF}=\frac{RS}{FG}=\frac{SP}{GD}

b)

PQGD=QRFG=RSEF=SPDE\frac{\text{PQ}}{GD}=\frac{QR}{FG}=\frac{RS}{EF}=\frac{SP}{DE}

c)

DERS=EFSP=FGPQ=QRGD\frac{DE}{RS}=\frac{EF}{SP}=\frac{FG}{PQ}=\frac{QR}{GD}

4.

The polygons are similar. Find the value of x.

a)

16

b)

4

c)

12

d)

3

5.

The polygons are similar. Find the value of x.

a)

12

b)

18

c)

24

d)

9

6.

Determine whether the polygons are similar. If they are write a similarity statement.

a)

No; corresponding angles are not congruent.

b)

ΔHJKΔLMN\Delta HJK\sim\Delta LMN

Yes;

c)

No, corresponding sides are not proportional.

7.

Determine if the polygons are similar. If so, write a similarity statement.

a)

No, corresponding angles are not congruent.

b)

Yes; ΔEFGΔDFH\Delta EFG\sim\Delta DFH

c)

No, corresponding sides are not proportional.

8.

The polygons are similar. The area of one triangle is given. Find the area of the other.

a)

100 cm2

b)

90 cm2

c)

86 cm2

d)

30 cm2

9.

The two polygons are similar. Find the ratio of the perimeters of RSTU to ABCD.

a)

2

b)

 34\frac{3}{4}  

c)

6

d)

 43\frac{4}{3}