Free Printable Year 10 Congruent & Similar Shapes

Free Printable Worksheets

Worksheets

Year 10 Congruent & Similar Shapes

Total questions: 57

Worksheet time: 2hrs 43mins

Name

Class

Date

1.

Figures that have the same _____ and size are congruent.

a)

corresponding

b)

corners

c)

angles

d)

shape

2.

a)

A

b)

C

c)

D

3.

a)

3 inches

b)

5 inches

c)

90 inches

d)

4 inches

4.

a)

A

b)

B

c)

C

d)

D

5.

a)

A

b)

B

c)

C

d)

D

6.

Two objects that are the same shape but not the same size are _______.

a)

Congruent

b)

Vertical

c)

Similar

d)

Complementary

7.

_{Line AB corresponds with what line?}

a)

XZ

b)

XY

c)

YZ

d)

YX

8.

Line AB corresponds with what line?

a)

ZV

b)

VW

c)

YX

d)

ZY

9.

If ΔABC ≅ ΔXYZ, which of the following angles correspond?

a)

<A ≅ < Z

b)

∠C ≅ ∠Z

c)

∠B ≅ ∠C

d)

<Z ≅ <B

10.

If ΔDEF ≅ ΔRST, then ∠S ≅ ____.

a)

∠F

b)

∠E

c)

∠D

d)

DE

11.

All angles in similar figures are congruent.

a)

True

b)

False

12.

Tell whether the two figures are similar. Explain your reasoning.

a)

Yes, similar because they are the same shape and side lengths are proportional.

b)

No, not similar because they are the same shape, but side lengths are not proportional.

c)

Yes, same shape

d)

No, different sizes

13.

The pair of figures is similar. Find the missing side.

a)

x = 20

b)

x = 12

c)

x = 5

d)

x = 4

14.

Which side length corresponds with EF?

a)

ML

b)

LM

c)

OL

d)

EH

15.

All triangles are similar to each other because they all have three sides

a)

False

b)

True

16.

Tell whether the two figures are congruent.

a)

Yes, same size and same shape

b)

No, same shape but different sizes

c)

No, different size and different shapes

17.

Tell whether the two figures are congruent.

a)

Yes, same size and same shape

b)

No, same shape but different sizes

c)

No, different size and different shapes

18.

Tell whether the two figures are similar. Explain your reasoning.

a)

Yes, similar because they are the same shape and side lengths are proportional.

b)

No, not similar because they are the same shape, but side lengths are not proportional.

c)

Yes, same shape

d)

No, different sizes

19.

Matching sides are called

a)

Corresponding Sides

b)

Corresponding Angles

c)

The Same

d)

Congruent Sides

20.

If two shapes have the same corresponding measurements...

a)

They're congruent only

b)

They're similar only

c)

They're similar and congruent

d)

There's no relationship

21.

Are the following similar? Why or why not?

a)

Yes

b)

No, the corresponding angles are not equal.

c)

No, the ratios of the corresponding sides are not equal.

22.

Determine the relationship of the figures.

a)

Congruent

b)

Not Congruent

c)

Similar

23.

Determine the relationship of the figures.

a)

Congruent

b)

Not Congruent

c)

Similar

24.

Determine the relationship of the figures.

a)

Congruent

b)

Not Congruent

c)

Similar

25.

Determine the relationship of the figures.

a)

Congruent

b)

Not Congruent

c)

Similar

26.

Determine the relationship of the figures.

a)

Congruent

b)

Not Congruent

c)

Similar

27.

Determine the relationship of the figures.

a)

Congruent

b)

Not Congruent

c)

Similar

28.

Determine the relationship of the figures.

a)

Congruent

b)

Not Congruent

c)

Similar

29.

Find missing side

a)

5

b)

7

c)

9

d)

11

30.

The pair of figures is similar. Find the missing side.

a)

x = 20

b)

x = 12

c)

x = 5

d)

x = 4

31.

Find the length of the missing side.

a)

7

b)

4

c)

6

d)

8

32.

Solve the proportion.

a)

k=5

b)

k=3.3333333

c)

k=60

d)

k=90

33.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

34.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

35.

Find the length of x

a)

x = 1

b)

x = 2

c)

x = 7

d)

x = 1/7

36.

Triangle ABC and XYZ are similar. Use your knowledge of scale factor to find the length of X.

a)

20

b)

25

c)

100

d)

40

37.

What is the scale factor if the triangle on the left is the original?

a)

2

b)

3/2

c)

2/3

d)

1/2

38.

The scale drawing car length is 3 cm. If the scale is 1 cm:4 ft, what is the actual car length?

a)

12 feet

b)

16 feet

c)

10 feet

d)

4 feet

39.

If the scale factor is greater than one, the new figure will be

a)

a reduction

b)

an enlargement

c)

a scale

d)

not proportional

40.

What is the scale factor from ΔDEF to ΔABC?

a)

1/2

b)

7/3

c)

2

d)

10/3

41.

What is the scale factor from ABCD to MNOP?

a)

2/3

b)

3/2

c)

2

d)

3

42.

What is the scale factor from MNOP to ABCD?

a)

2/3

b)

1/2

c)

3/2

d)

2

43.

The distance between two cities on a map is 4.125 inches. Find the actual distance if the scale on the map is 2 inches = 40 miles.

a)

165 miles

b)

50 miles

c)

82.5 miles

d)

41.25 miles

44.

A scale drawing that measures 8 units wide and an original that measures 4 units wide has a scale factor of...

a)

2:1

b)

8:1

c)

bigger

d)

1:2

45.

If the original is 12 units and the scale factor is 1/4 what is the size of the scale drawing?

a)

300

b)

4.8

c)

3

d)

4

46.

Are the rectangular cakes are scale drawings of each other.
Cake 1: (5, 3), (5, 5), (11,3), (11, 5)
Cake 2: (1, 6), (1, 12), (13, 12), (13, 6)
How do you know?

a)

yes sides are in proportion

b)

no there is no factor that could be multiplied and get corresponding answers

c)

no because their areas are different

d)

yes because they look llike it

47.

If the original lengths are multiplied by 2, what are the new coordinates?

a)

(0, 0), (12, 18), (12, 0)

b)

(0, 0), (18, 12), (12, 0)

c)

(0, 0), (12, 18), (0, 12)

d)

(0, 0), (18, 12), (0, 12)

48.

What are the actual dimensions of this rectangle if 1cm =5ft

a)

25 ft by 20 ft

b)

1 ft by 0.8 ft

c)

5 ft by 4 ft

d)

10 ft by 8 ft

49.

What is the area of this rectangle?

a)

17.05cm²

b)

17.2cm²

c)

8.6cm²

d)

12.5cm²

50.

If I wanted to create a scale drawing 1/5 of the size, what would be the new dimensions?

a)

0.4m by 0.6m

b)

10m by 15m

c)

8m by 12m

d)

4m by 6m

51.

If 1 foot = 3 inches, what would be the area of this rectangle in inches?

a)

27in²

b)

42in²

c)

162in²

d)

1620in²

52.

If 1 foot = 3 inches, what would be the perimeter of this rectangle in inches?

a)

27in

b)

42in

c)

162in

d)

1620in

53.

If the scale used is 4in=1ft, what would be the area of this rectangle?

a)

0.5ft²

b)

1.2ft²

c)

0.6ft²

d)

3.4ft²

54.

What is the area of this rectangle?

a)

4.07cm²

b)

8.1cm²

c)

6.4cm²

d)

5.03cm²

55.

What is the perimeter of this rectangle?

a)

4.07cm

b)

8.1cm

c)

6.4cm

d)

5.03cm

56.

If every block represents 12 feet, what is the area of this rectangle?

a)

28ft²

b)

48ft²

c)

6,912ft²

d)

336ft²

57.

If every block represents 12 feet, what is the perimeter of this rectangle?

a)

28ft

b)

48ft

c)

6,912ft

d)

336ft

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