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Similar Triangles

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Similar Triangles

- Are Enlargements of each other
- Corresponding angles are equal
- Sides are related by the same scale factor

Triangles are similar if matching

angles remain the same size.

100º

30º

50º

100º

30º

50º

10º

50º

120º

120º

10º

50º

5

15

5

4

x 3

x 3

6

Scale factor 3

15

12

1

3

18

Scale factor 1/3

A

D

E

C

B

3

4

6

Triangle ABC is similar to triangle ADE.

DE is parallel to BC.

Calculate the length of BC

3

4

E

D

A

9

6

C

12

B

9

3

x 3

AB & DE are parallel

Explain why ABC is similar to CDE

<CED = <BAC Alternate Angles

5

A

B

<EDC = <ABC Alternate Angles

<ECD = <ACB Vert Opp Angles

3

C

6

E

D

?

Triangle ABC is similar to Triangle CDE

Calculate the length of DE

AC corresponds to CE

Scale Factor = 2

5

A

B

AB corresponds to DE

DE = 2 x AB

3

C

DE = 10cm

6

E

D

?

- To calculate missing sides, we first of all need the scale factor
- We then either multiply or divide by the scale factor
- To show that 2 shapes are similar we can either show that all of the sides are connected by the scale factor or show that matching angles are the same