Transcript PPT: Similar Triangles

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
Show that these triangles are similar
10º
50º
120º
10º
50º
120º
To calculate a length
15
5x
5
3
4
x3
6
Scale factor 3
15
1
3
18
Scale factor 1/3
12
Harder example
A
3
4
D
E
6
C
B
Triangle ABC is similar to triangle ADE.
DE is parallel to BC.
Calculate the length of BC
Harder example
A
D
3
4
E
9
6
B
C
12
9x
3
3
…and then…
AB & DE are parallel
Explain why ABC is similar to CDE
5
A
B
<CED = <BAC Alternate Angles
<EDC = <ABC Alternate Angles
<ECD = <ACB Vert Opp Angles
3
C
6
E
D
?
Triangle ABC is similar to Triangle CDE
…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
• 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