similar triangles

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

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

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

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

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

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

9. …and then…
A
C
E
D
B
3
6
5
?
Calculate the length of DE
Scale Factor = 2
AC corresponds to CE
AB corresponds to DE
DE = 2 x AB
DE = 10cm

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