in geometry, two objects are similar when one is a scale model of the other. similar shapes

In geometry, two objects are similar when one is a scale model of the other.

SIMILAR SHAPES

These two triangles appear to be similar….

SIMILAR SHAPES

SIMILAR SHAPES

These two are NOT similar….

How do you check that triangles are similar?

SIMILAR TRIANGLES

We need to compare CORRESPONDING sides….

SIMILAR TRIANGLES

….or corresponding angles.

SIMILAR TRIANGLES

Corresponding angles will be equal.

26

12 2

4

8 2

5

10

Looking for a scale factor

8

10

6

15

912

SIMILAR TRIANGLES

These two triangles are similar. What is the scale factor?

8

10

6

15

912

SIMILAR TRIANGLES

We really only need to use one pair of corresponding sides.

SF = 12 ÷ 8 = 1.5

SIMILAR TRIANGLES

Are these triangles similar?

d

c

b

a adbc

4

6

6

8

8

10

Does the following apply?

Try this neat method...

If this is true, similarity applies

4

6

6

8

8

10

Lets check...

So these are not similar triangles

88106

The two triangles are similar. Use the cross multiplying method to determine the missing value x.

12

X

15

18

x

18

15

12

27012

151812

x

x

5.22

12270

x

x