# Similar Shapes

Two figures, which have the same shape, are considered as similar shapes. When any two figures are similar, then their ratio of length to their sides respectively are equal.

For identifying whether the shapes are similar or not, compare their sides respectively. Two shapes are considered similar to each other, if one can become similar to the first one after the turn, reshaping and flipping and sliding, then both shapes are considered similar.

## Concept

When two shapes are said to be similar, they share the following characteristics:

• All the angles are the same
• All the lines are said to be in proportion https://www.mathsisfun.com/geometry/triangles-similar.html

### Example 1: Find The Scale Factor Triangle ABC and DEF are similar. What is the scale factor?

Step 1: Pick a corresponding side:

• BC and EF
• AC and DF
• AB and DE

Since the sides BC and EF are known, we will pick these sides.

Step 2: Divide the corresponding sides:

• BC/EF = 9/5 = 1.8 ←- scale factor

### Example 2: Find The Missing Side

Using the same problem from above, find side AC.

Step 1: Find scale factor (see procedure from previous problem)

Step 2: To find the side AC, we have to multiply DF by the scale factor:

AC = DE * scale factor = 3 * (9/5) = 5.4

Step 3 (Optional): Verify scale factor.

Divide each corresponding side to see if the scale factor is the same:

• BC/EF = 9/5 = 1.8
• AC/DF = 5.4/3 = 1.8

Scale factor has been verified.

### Example 3 : Find The Missing Side Triangle ABC and DEF are similar. Find side X and Y.

Step 1: Find scale factor

• AB and DE
• BC and EF (side X)
• AC and DF (side Y)

Since the sides AB and DE are known, we will chose those sides.

Divide corresponding sides:

AB/DE = 6/4 = 1.5 ←-scale factor

Step 2: To find X, divide the corresponding side BC by the scale factor:

BC / scale factor = 7 / (6/4) = 4.666

Step 3: To find side Y, divide the corresponding side AC by the scale factor:

AC / scale factor = 8 / (6/4) = 5.333

Step 3 (Optional): Verify scale factors:

• AB/DE = 6/4 = 1.5
• BC/EF = 7/4.666 = 1.5
• AC/DF = 8/5.333 = 1.5

Scale factor has been verified.