1. Similar Triangles

2. Similar shapes Are Enlargements of each other
Corresponding angles are equal
Sides are related by the same scale factor

3. Similar Triangles Triangles are similar if matching
angles remain the same size.
100º
30º
50º
100º
30º
50º

4. Show that these triangles are similar
10º
50º
120º
120º
10º
50º

5. x 3 x 3 To calculate a length 15 5 1 3 5 4 6 15 12 18 Scale factor 3

6. Harder example C A E D B 3 4 6
Triangle ABC is similar to triangle ADE.
DE is parallel to BC.
Calculate the length of BC

7. Harder example A E D 3 4 9 6 12 C B 9 3
x 3

8. …and then… AB & DE are parallel Explain why ABC is similar to CDE 5
<CED = <BAC Alternate Angles A B
<EDC = <ABC Alternate Angles
<ECD = <ACB Vert Opp Angles 3 C 6 D E ?
Triangle ABC is similar to Triangle CDE

9. …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 D E ?

10. 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