Congruence and Similarity 3

Congruence and Similarity 3

Learning Goal

To be able to apply scale factors to calculate unknown sides in similar figures 

Similar Figures

Similar figures have the same shape, but not necessarily the same size.

Examples of similar shapes

Similar figures must have:

1. Corresponding sides are proportional (have a constant ratio, called the scale factor)

In the diagram: from the smaller triangle to larger triangle, the scale factor is 3

Similar figures must have:

2. Corresponding angles are equal. 

Similar shapes must have:

• Corresponding sides are proportional

• Corresponding angles are equal

It is possible to transform a figure by increasing or decreasing the original figure. The resulting figure is known as the image. 

Multiple Choice

Are the two shapes in the diagram similar?

• Yes

• No

Multiple Choice

Are the two shapes in the diagram similar

?

• Yes

• No

Multiple Choice

Are the pair of shapes in the diagram similar?

• Yes

• No

In the following diagram,

triangle ABC is similar to triangle DEF (ΔABC ~ ΔDEF)

since ∠ABC = ∠DEF,

∠BAC = ∠EDF and

∠ACB = ∠DFE

Calculating scale factor

Fill in the Blanks

Fill in the Blanks