Transcript Similar Triangles I

SIMILAR SHAPES
In geometry, two objects are similar when
one is a scale model of the other.
SIMILAR SHAPES
These two triangles appear to be similar….
SIMILAR SHAPES
These two are NOT similar….
SIMILAR TRIANGLES
How do you check that triangles are similar?
SIMILAR TRIANGLES
We need to compare CORRESPONDING
sides….
SIMILAR TRIANGLES
….or corresponding angles.
Corresponding angles will be equal.
Looking for a scale factor
12
2
6
8
2
4
10
2
5
SIMILAR TRIANGLES
These two triangles are similar. What is the
scale factor?
8
10
6
12
9
15
SIMILAR TRIANGLES
We really only need to use one pair of
corresponding sides.
8
6
12
10
SF = 12 ÷ 8 = 1.5
9
15
SIMILAR TRIANGLES
Are these triangles similar?
Does the following apply?
10 8 6
 
8 6 4
Try this neat method...
a c

b d
bc  ad
If this is true, similarity applies
Lets check...
10 8 6
 
8 6 4
6  10  8  8
So these are not similar triangles
The two triangles are similar. Use the
cross multiplying method to determine
the missing value x.
15
12
18
X
12 18

15 x
12x  18 15
12x  270
x  270  12
x  22.5