# What is the definition of a similar shape?

## What is the definition of a similar shape?

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.

**How do you prove shapes are similar?**

If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

### What are congruent and similar shapes?

Two identical 2D shapes are said to be congruent. Two 2D shapes that share the same proportions are similar. The angles and side lengths can help us decide which type they are.

**How do you work out similar triangles?**

Calculating the Lengths of Corresponding Sides

- Step 1: Find the ratio. We know all the sides in Triangle R, and. We know the side 6.4 in Triangle S.
- Step 2: Use the ratio. a faces the angle with one arc as does the side of length 7 in triangle R. a = (6.4/8) × 7 = 5.6.

#### How are two shapes similar in size and shape?

They are identical in size and shape. When a shape is enlarged, the image is similar to the original shape. It is the same shape but a different size. These two shapes are similar as they are both rectangles but one is an enlargement of the other.

**When are two shapes of the same size are congruent?**

Scale factors show how much larger or smaller similar shapes are. Two shapes that are the same size and the same shape are congruent. Shapes A, B, E and G are congruent. They are identical in size and shape. When a shape is enlarged, the image is similar to the original shape. It is the same shape but a different size.

## How does the size of a shape change?

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. When a shape is enlarged, the image is similar to the original shape.

**How to calculate the missing length of a similar shape?**

Angle DBE = angle ABC because both triangles share the same angle. All three angles are the same in both triangles so they are similar. To calculate a missing length, draw the two triangles separately and label the lengths. To calculate the scale factor, divide the two corresponding lengths. The scale factor of enlargement is 1.5.