Similar triangles
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Similar Triangles PowerPoint PPT Presentation


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Similar Triangles. Similar shapes. Are Enlargements of each other Corresponding angles are equal Sides are related by the same scale factor. Similar Triangles. Triangles are similar if matching angles remain the same size. 100º. 30º. 50º. 100º. 30º. 50º.

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Similar Triangles

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Similar triangles

Similar Triangles


Similar shapes

Similar shapes

  • Are Enlargements of each other

  • Corresponding angles are equal

  • Sides are related by the same scale factor


Similar triangles1

Similar Triangles

Triangles are similar if matching

angles remain the same size.

100º

30º

50º

100º

30º

50º


Show that these triangles are similar

Show that these triangles are similar

10º

50º

120º

120º

10º

50º


To calculate a length

To calculate a length

5

15

5

4

x 3

x 3

6

Scale factor 3

15

12

1

3

18

Scale factor 1/3


Harder example

A

D

E

C

B

Harder example

3

4

6

Triangle ABC is similar to triangle ADE.

DE is parallel to BC.

Calculate the length of BC


Harder example1

3

4

E

D

Harder example

A

9

6

C

12

B

9

3

x 3


And then

…and then…

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


And then1

…and then…

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

?


Summary similar shapes

Summary – Similar shapes

  • 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


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