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
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
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
6
Harder example
3
4
6
Triangle ABC is similar to triangle ADE. DE is
parallel to BC. Calculate the length of BC
7
Harder example
A
9
6
C
12
B
9 3
x 3
8
and then
AB DE are parallel
Explain why ABC is similar to CDE
5
ltCED ltBAC Alternate Angles
A
B
ltEDC ltABC Alternate Angles
ltECD ltACB Vert Opp Angles
3
C
6
E
D
?
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
E
D
?
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