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Lesson: Similar Triangles
Contributed by: Moore
(Original author: Pappal)
Congruent triangles
Congruent triangles
are triangles that have the same size and shape.
Congruent triangles
are triangles that have the same size and shape.
Congruent triangles
Similar triangles
are triangles that have the same size and shape.
Congruent triangles
Similar triangles
are triangles that have the same size and shape.
Congruent triangles
Similar triangles
have the same shape but different sizes.
Congruent
?
Similar
?
How do we know when triangles are similar?
How do we know when triangles are similar?
2
5
4
1
2.5
2
How do we know when triangles are similar?
Their corresponding angles have to be exactly the same.
2
5
4
1
2.5
2
How do we know when triangles are similar?
Their corresponding angles have to be the same.
2
5
4
1
2.5
2
This symbol means 
the angles have the 
same value.
How do we know when triangles are similar?
Their corresponding angles must have the same values.
2
5
4
1
2.5
2
These angles are 
the same.
How do we know when triangles are similar?
Their corresponding angles must have the same value.
2
5
4
1
2.5
2
These angles 
are the same.
Their corresponding sides have to be proportional.
How do we know when triangles are similar?
Their corresponding angles must have the same values.
2
5
4
1
2.5
2
Their corresponding sides have to be proportional.
How do we know when triangles are similar?
Their corresponding angles must have the same values.
(Proportional means they have to divide to the
same thing.)
2
5
4
1
2.5
2
Their corresponding sides have to be proportional.
How do we know when triangles are similar?
Their corresponding angles must have the same value.
2
5
4
1
2.5
2
4 ÷ 2 = 2
Their corresponding sides have to be proportional.
How do we know when triangles are similar?
Their corresponding angles must have the same value.
2
5
4
1
2.5
2
4 ÷ 2 = 2
2 ÷ 1 = 2
Their corresponding sides have to be proportional.
How do we know when triangles are similar?
Their corresponding angles must have the same values.
2
5
4
1
2.5
2
4 ÷ 2 = 2
2 ÷ 1 = 2
5 ÷ 2.5 = 2
Their corresponding sides have to be proportional.
How do we know when triangles are similar?
Their corresponding angles must have the same values.
2
5
4
1
2.5
2
4 ÷ 2 = 2
2 ÷ 1 = 2
5 ÷ 2.5 = 2
Their corresponding sides have to be proportional.
How do we know when triangles are similar?
Their corresponding angles must have the same values.
2
5
4
1
2.5
2
4 ÷ 2 = 2
2 ÷ 1 = 2
5 ÷ 2.5 = 2
All the same
For shapes to be similar
their corresponding angles must be
their corresponding sides must be
proportional
?
the same
?
We can use similarity
We can use similarity
to find unknown sides
We can use similarity
to find unknown sides
2
5
x
10
We can use similarity
to find unknown sides
2
5
x
10
corresponding sides
These are
We can use similarity
to find unknown sides
2
5
x
10
corresponding sides
These are
We can use similarity
to find unknown sides
2
5
x
10
2
x
=
10
5
We can use similarity
to find unknown sides
2
5
x
10
Solve
2
x
=
10
5
We can use similarity
to find unknown sides
2
5
x
10
Solve
2
x
5x = 20
=
10
5
We can use similarity
to find unknown sides
2
5
x
10
Solve
2
x
5x = 20
x = 4
=
10
5
x
x =
5
8
10
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