Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.

Question

Identify if the two shapes are congruent, similar, both, or neither. Round your answer to the nearest tenth if necessary. 9in 6in 3in 2in
A.Similar

B.Congruent

C.Neither

D.Both

Best answer

Answer 1

To determine whether the two shapes are congruent, similar, both, or neither based on the given measurements (9 in, 6 in, 3 in, 2 in), let's analyze the information.

1. Congruent Shapes: Two shapes are congruent if they are exactly the same size and shape. This means all corresponding sides and angles must be equal.

2. Similar Shapes: Two shapes are similar if their corresponding angles are equal, and the lengths of their corresponding sides are in proportion (the ratio of the lengths of corresponding sides is constant).

Given the lengths provided (9 in, 6 in, 3 in, 2 in), we can calculate the ratios between the corresponding sides:

Let's assume you have two rectangles:

• Rectangle 1 sides: 9 in and 6 in
• Rectangle 2 sides: 3 in and 2 in

Now, let's find the ratios of the lengths:

For Rectangle 1:

• The ratio of one side is 9/3 = 3
• The ratio of the other side is 6/2 = 3

Both ratios are equal (3:1), which indicates that the two rectangles have the same shape, meaning the two figures are similar.

They are not congruent since they are not the same size (the lengths of corresponding sides differ).

So the answer is:

A. Similar