Question

use the graphed polygons a - f to answer the questions below:

1. ____ figure a is similar to a by a scale factor of...

a) 0 b) 1/2
c) 1 d) 2
e) 1/3 f) 3
g) 4 h) not similar

1. ____ figure a is similar to b by a scale factor of...

a) 0 b) 1/2
c) 1 d) 2
e) 1/3 f) 3
g) 4 h) not similar

1. ____ figure a is similar to c by a scale factor of...

a) 0 b) 1/2
c) 1 d) 2
e) 1/3 f) 3
g) 4 h) not similar

1. ____ figure a is similar to d by a scale factor of...

a) 0 b) 1/2
c) 1 d) 2
e) 1/3 f) 3
g) 4 h) not similar

1. ____ figure a is similar to e by a scale factor of...

a) 0 b) 1/2
c) 1 d) 2
e) 1/3 f) 3
g) 4 h) not similar

1. ____ figure a is similar to f by a scale factor of...

a) 0 b) 1/2
c) 1 d) 2
e) 1/3 f) 3
g) 4 h) not similar

Explanation:

Step1: Recall the definition of similar polygons

Similar polygons have the same shape but not necessarily the same size. The scale factor is the ratio of corresponding side lengths.

Step2: Analyze each pair

• For figure A and A:

The scale factor of a figure to itself is \(1\) because all corresponding side lengths are equal.

• For figure A and B:

They are not similar as their shapes do not match in terms of angle - side relationships.

• For figure A and C:

They are not similar as their shapes do not match in terms of angle - side relationships.

• For figure A and D:

They are not similar as their shapes do not match in terms of angle - side relationships.

• For figure A and E:

They are not similar as their shapes do not match in terms of angle - side relationships.

• For figure A and F:

They are not similar as their shapes do not match in terms of angle - side relationships.

Answer:

1. c) 1
2. h) NOT SIMILAR
3. h) NOT SIMILAR
4. h) NOT SIMILAR
5. h) NOT SIMILAR
6. h) NOT SIMILAR