Similarity (As a Size Transformation) — Multiple Choice Questions

Figures which have exactly the same shape, but not necessarily the same ............... are said to be similar.

1. angle

2. side

3. size

4. volume

Answer

Figures are said to be similar if: their shapes are identical,but their sizes may differ.

Hence, option 3 is the correct option.

All regular polygons having the same number of ............... are similar.

1. sides

2. angles

3. diagonals

4. centric

Answer

All regular polygons with the same number of sides are always similar, regardless of their size.

Hence, option 1 is the correct option.

Two circles are always :

1. congruent

2. similar

3. enlarged

4. concentric

Answer

Two circles are always similar because similarity means that the figures have the same shape but possibly different sizes.

Hence, option 2 is the correct option.

In size transformation, the given figure is called an object and the resulting figure is called its :

1. pre-image

2. image

3. post-image

4. enlarge object

Answer

The resulting figure, after the transformation is applied, is called the image.

Hence, option 2 is the correct option.

Let k be the scale factor of a given size transformation. Then k < 1 as the transformation is a/an :

1. enlargement

2. identity transformation

3. reduction

4. preserved

Answer

If the transformation is a reduction, the image is smaller than the object, meaning the scale factor k is between 0 and 1: 0 < k < 1.

Hence, option 3 is the correct option.

Each side of the resulting figure = ............... times the corresponding side of the given figure, where k is the scale factor.

1. k²

2. k

3. k³

4. 2k

Answer

The length of any side in the resulting figure (the image) is equal to the length of the corresponding side in the given figure (the object) multiplied by the scale factor k.

Hence, option 2 is the correct option.

The transformation is a/an ..............., if k = 1, where k is the scale factor of a given size transformation.

1. identity transformation

2. reduction

3. enlargement

4. map

Answer

If k = 1, the resulting figure (image) is congruent to the original figure (object), meaning it has the same size and the same shape. This specific transformation is called an identity transformation because it maps the object onto itself.

Hence, option 1 is the correct option.

In case of solids, we have volume of the resulting figure = ............... × (volume of the given figure), where k is the scale factor.

1. k

2. k²

3. k³

4. 3k

Answer

Volume of the resulting figure = k³ × (the volume of given figure)

Hence, option 3 is the correct option.

If scale factor, k = $\dfrac{1}{p}$, then area of the model = ............... × (area of the actual figure).

1. k²

2. k

3. k³

4. $\dfrac{1}{p}$

Answer

We know that,

If scale factor = k, then :

Area of model = k² × (Area of actual figure)

Hence, option 1 is the correct option.

Let the map of a plane figure be drawn to the scale 1 : p. Then scale factor, k = ..............., length in the map = k × (Actual length).

1. $\dfrac{p}{1}$

2. $\dfrac{1}{p}$

3. $\dfrac{1}{k}$

4. k

Answer

Given,

Scale = 1 : p = $\dfrac{1}{p}$.

Hence, option 2 is the correct option.

The scale factor of a picture and the actual height of Sonia is 20 cm : 1.6 m. If her height in the picture is 18 cm, then her actual height is:

1. 14.4 m

2. 2.25 m

3. 1.78 m

4. 1.44 m

Answer

Scale factor of a picture and the actual height = 20 cm : 1.6 m = 20 cm : 160 cm

$\therefore \dfrac{\text{Height in picture}}{\text{Actual height}} = \dfrac{\text{20 cm}}{\text{160 cm}} \\[1em] \Rightarrow \dfrac{18}{\text{Actual height}} = \dfrac{\text{20 cm}}{\text{160 cm}} \\[1em] \Rightarrow \text{Actual height} = \dfrac{18 \times 160}{20} = \text{144 cm} = 1.44 \text{ m}.$

Hence, option 4 is the correct option.