Geometric Similarity: Master the Concept of Similar Figures

Question 1

If two triangles share the same shape but differ in size, how are their corresponding sides related?

Accepted Answer

Proportional

Answer

Equal

Answer

Inversely proportional

Answer

Squared

Question 2

Given parallelogram ABCD with vertices A(2, 3), B(5, 7), C(8, 4), D(5, 1), and parallelogram EFGH with vertices E(9, 6), F(12, 10), G(15, 7), H(12, 3), determine if the parallelograms are similar.

Accepted Answer

Yes, they are similar.

Answer

No, they are not similar.

Answer

Cannot be determined.

Question 3

Which of the following statements about the area of similar figures is true?

Accepted Answer

The ratio of their areas is equal to the ratio of their side lengths squared

Answer

The ratio of their areas is equal to the ratio of their perimeters squared

Answer

The area of one figure is always double the area of the other

Answer

The area of one figure can never be greater than the area of the other

Question 4

In two similar triangles, the ratio of their corresponding medians is:

Accepted Answer

Equal to the ratio of their corresponding side lengths

Answer

Equal to the ratio of their corresponding angles

Answer

Equal to the ratio of the areas of the triangles

Answer

Equal to 1

Question 5

In a dilation with a scale factor of 1.5, what is the ratio of the image's side length to the preimage's side length?

Accepted Answer

1.5:1

Answer

1:1.5

Answer

1:2.25

Answer

2.25:1

Question 6

Which transformation always results in the creation of similar figures?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 7

Which statement accurately describes similar figures?

Accepted Answer

They have the same shape but can have different sizes.

Answer

They have the same size but can have different shapes.

Answer

They have the same area but can have different perimeters.

Answer

They have the same volume but can have different surface areas.

Question 8

In a dilation with a scale factor of 1/2, the image is:

Accepted Answer

Half the size of the pre-image

Answer

Twice as large as the pre-image

Answer

The same size as the pre-image

Answer

Cannot be determined

Question 9

Which statement is NOT a property of similar figures?

Accepted Answer

Diagonals are parallel

Answer

Corresponding angles are congruent

Answer

Corresponding sides are proportional

Answer

Areas are proportional to the squares of the corresponding sides

Question 10

Similar figures have the same shape but not necessarily the same size. Which of the following statements accurately describes this definition?

Accepted Answer

True

Answer

False

Answer

Applies only to equilateral triangles

Answer

True only if the triangles are congruent

Question 11

To find the scale factor between two similar figures, we use:

Accepted Answer

The ratio of their corresponding sides

Answer

The ratio of their areas

Answer

The ratio of their perimeters

Answer

The sum of their side lengths

Question 12

Which property is NOT shared by similar figures?

Accepted Answer

Equal perimeters

Answer

Same shape

Answer

Corresponding angles equal

Answer

Corresponding sides proportional

Question 13

If the ratio of the corresponding sides of two similar trapezoids is 3:4, then the ratio of their areas is:

Accepted Answer

9:16

Answer

3:4

Answer

4:3

Answer

16:9

Question 14

The side of a rectangle measures 5 cm. If the rectangle is enlarged by a scale factor of 3, what is the length of a side of the enlarged rectangle?

Accepted Answer

15 cm

Answer

5 cm

Answer

10 cm

Answer

20 cm

Question 15

Which statement about similar triangles is accurate?

Accepted Answer

Their corresponding altitudes are proportional.

Answer

Their corresponding medians are proportional.

Answer

Their corresponding bisectors are proportional.

Question 16

In a pair of similar figures, the ratio of the perimeters is 2:3. If the perimeter of the smaller figure is 24 units, what is the perimeter of the larger figure?

Accepted Answer

36 units

Answer

32 units

Answer

48 units

Answer

54 units

Question 17

Which type of triangles can be proven similar using the Pythagorean Theorem?

Accepted Answer

Right triangles

Answer

Isosceles triangles

Answer

Scalene triangles

Answer

Equilateral triangles

Question 18

Identify the pair of figures that are not similar.

Accepted Answer

Two circles with different radii

Answer

Two rectangles with equal side lengths

Answer

Two squares with equal side lengths

Answer

Two equilateral triangles with different side lengths

Question 19

Determine if the statement is true or false: Two circles can be similar.

Accepted Answer

True

Answer

False

Question 20

If two triangles have equal corresponding angles, are they necessarily similar?

Accepted Answer

Yes

Answer

No

Question 21

Determine if the statement is true or false: The scale factor between two similar figures can be a fraction.

Accepted Answer

True

Answer

False

Question 22

Which transformation preserves the shape and size of a figure?

Accepted Answer

Dilation with scale factor 1

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 23

Two circles are similar if they have:

Accepted Answer

Proportional circumferences

Answer

Congruent radii

Answer

Equal diameters

Answer

Identical areas

Question 24

In a dilation with a scale factor of 0.5, the image is:

Accepted Answer

Half the size of the original

Answer

Twice the size of the original

Answer

Half the perimeter of the original

Answer

Twice the area of the original

Question 25

Which transformation can produce similar but not congruent figures?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 26

Two similar rectangles have a scale factor of 3. What is the ratio of their areas?

Accepted Answer

9:1

Answer

1:3

Answer

3:1

Answer

1:9

Question 27

Which of the following statements about similar figures is true?

Accepted Answer

They have the same shape but not necessarily the same size

Answer

They have the same size but not necessarily the same shape

Answer

They have the same angles but not necessarily the same side lengths

Answer

They have the same side lengths but not necessarily the same angles

Question 28

Which of the following is NOT a criterion for similarity in triangles?

Accepted Answer

All sides are congruent.

Answer

Corresponding angles are congruent.

Answer

Corresponding sides are proportional.

Answer

The triangles have the same shape.

Question 29

Two similar polygons have areas of 36 square inches and 144 square inches. The larger polygon has a perimeter of 48 inches. What is the perimeter of the smaller polygon?

Accepted Answer

16 inches

Answer

12 inches

Answer

24 inches

Answer

36 inches

Question 30

In a dilation with a scale factor of 2, the image of the point (3, -5) is:

Accepted Answer

(6, -10)

Answer

(3, -10)

Answer

(6, -5)

Answer

(1, -2.5)

Question 31

If a figure is enlarged by a scale factor of 3, what is the ratio of the area of the enlarged figure to the area of the original figure?

Accepted Answer

9

Answer

3

Answer

6

Answer

12

Question 32

Which transformation does NOT preserve similarity?

Accepted Answer

Shear

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 33

Two squares have equal side lengths. Which statement is true?

Accepted Answer

They must be similar.

Answer

They must have different perimeters.

Answer

They must have different areas.

Answer

They can have different orientations.

Question 34

A dilation maps a line segment of length 6 units to a segment of length 12 units. What is the scale factor of the dilation?

Accepted Answer

2

Answer

1/2

Answer

1/6

Answer

6

Question 35

A photograph with dimensions 3 inches x 5 inches is enlarged by a scale factor of 1.5. What are the dimensions of the enlarged photograph?

Accepted Answer

4.5 in. x 7.5 in.

Answer

4.5 in. x 5 in.

Answer

3 in. x 7.5 in.

Answer

7.5 in. x 5 in.

Question 36

Which statement about similar triangles is true?

Accepted Answer

Their areas are in the ratio of the squares of their corresponding side lengths.

Answer

Their altitudes are proportional.

Answer

Their perimeters are equal.

Answer

Their circumferences are proportional.

Question 37

A scale drawing of a building is drawn to a scale of 1:200. If the drawing shows a room with dimensions of 5 cm x 7 cm, what are the actual dimensions of the room?

Accepted Answer

2 m x 3.5 m

Answer

10 m x 14 m

Answer

15 m x 21 m

Answer

25 m x 35 m

Question 38

Two similar figures have a ratio of corresponding sides of 1:3. What is the scale factor between these figures?

Accepted Answer

1:3

Answer

3:1

Answer

1:9

Question 39

Which of the following is a necessary condition for two geometric figures to be considered similar?

Accepted Answer

Corresponding angles are congruent.

Answer

Corresponding sides are congruent.

Answer

They have the same number of sides.

Answer

They have equal areas.

Question 40

If the scale factor between two similar triangles is 3:2, what is the ratio of the perimeter of the larger triangle to the perimeter of the smaller triangle?

Accepted Answer

9:4

Answer

3:2

Answer

2:3

Answer

4:9

Question 41

If the side lengths of a triangle are increased by a factor of 3, what is the effect on the area of the triangle?

Accepted Answer

The area increases by a factor of 9.

Answer

The area increases by a factor of 3.

Answer

The area increases by a factor of 6.

Answer

The area increases by a factor of 12.

Question 42

Which statement accurately describes similar figures?

Accepted Answer

They have the same shape but not necessarily the same size.

Answer

They have the same size but not necessarily the same shape.

Answer

They have both the same shape and the same size.

Answer

They have neither the same shape nor the same size.

Question 43

Which property describes similar figures: equal shape but different sizes?

Accepted Answer

Equal shape

Answer

Equal perimeter

Answer

Equal area

Answer

Equal scale factor

Question 44

Which transformation below does NOT maintain similarity?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 45

Calculate the scale factor between two squares with respective side lengths of 4 cm and 8 cm.

Accepted Answer

2:1

Answer

1:2

Answer

1:4

Answer

4:1

Question 46

Given two similar triangles, one with an area of 6 square units and the other with an area of 54 square units, determine the scale factor.

Accepted Answer

3:1

Answer

1:3

Answer

1:6

Answer

6:1

Question 47

Which statement accurately describes the corresponding angles of similar polygons?

Accepted Answer

They are equal.

Answer

They are supplementary.

Answer

They are complementary.

Answer

They are alternate interior.

Question 48

Identify the characteristic that distinguishes similar figures:

Accepted Answer

Same shape, different size

Answer

Same size, different shape

Answer

Same shape and size

Answer

Different shape and size

Question 49

Which transformation does NOT preserve similarity?

Accepted Answer

Stretching

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 50

Two circles are similar. If the area of one is 100π sq cm, and the scale factor between them is 2, what's the area of the other?

Accepted Answer

400π sq cm

Answer

25π sq cm

Answer

50π sq cm

Answer

800π sq cm

Question 51

A rectangular prism has a scale factor of 1:3 compared to another similar rectangular prism. If the height of the larger prism is 12 cm, what's the height of the smaller prism?

Accepted Answer

4 cm

Answer

2 cm

Answer

6 cm

Answer

8 cm

Question 52

Which is NOT an application of similarity in real-world scenarios?

Accepted Answer

Calculating probability

Answer

Creating scale models

Answer

Designing buildings

Answer

Estimating distances

Question 53

Which statement about similarity transformations is true?

Accepted Answer

Preserve both angles and distances

Answer

Preserve angles but not distances

Answer

Preserve distances but not angles

Answer

Preserve neither angles nor distances

Question 54

Which property below is NOT characteristic of similar figures?

Accepted Answer

Equal dimensions

Answer

Identical shape

Answer

Proportional sides

Answer

Equivalent angles

Question 55

Given two right triangles with side lengths 3, 4, 5 and 6, 8, 10 respectively, find the scale factor between the triangles.

Accepted Answer

3/2

Answer

2/3

Answer

1/2

Answer

2/1

Question 56

A rectangle has a length of 10 cm and a width of 5 cm. If a similar rectangle has a length of 15 cm, what is its width?

Accepted Answer

7.5 cm

Answer

5 cm

Answer

10 cm

Answer

12.5 cm

Question 57

Given two similar triangles with corresponding angles measuring 45°, 60°, and 75°, what are the angles of the other triangle?

Accepted Answer

45°, 60°, 75°

Answer

60°, 75°, 45°

Answer

75°, 45°, 60°

Answer

30°, 45°, 60°

Question 58

Which option in the list below is NOT a real-world application of similarity?

Accepted Answer

Calculating the volume of cones

Answer

Creating maps

Answer

Designing buildings

Answer

Measuring distances in astronomy

Question 59

If a scale drawing of a house measures 6 inches in height and the actual height of the house is 24 feet, what is the scale factor of the drawing?

Accepted Answer

1/48

Answer

48

Answer

1/480

Answer

480