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Mathematic
(Preliminary)
Congruent Triangles
Stage 6 - Year 11
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1
Congruent Triangles 1
Two triangles are congruent if they are both
the same size and shape.
For Example
70o
6cm
75o
7cm
8cm
35o
70o
6cm
75o
7cm
8cm
35o
2
Congruent Triangles 2
Two triangles are congruent if.
All the three Sides of the triangles
are equal in length.
SSS
8cm
6cm
7cm
8cm
6cm
7cm
3
Congruent Triangles 3
Two triangles are congruent if.
Two pairs of corresponding Sides
and the included Angle are equal.
70o
6cm
SAS
8cm
6cm
70o
8cm
4
Congruent Triangles 4
Two triangles are congruent if.
Two pairs of Angles and any pair of
corresponding Sides are equal.
70o
75o
AAS
8cm
70o
8cm
75o
5
Congruent Triangles 5
Two triangles are congruent if.
Both have a Right angle. The Hypotenuses and
one pair of corresponding Sides are equal.
RHS
8cm
7cm
8cm
7cm
6
Congruent Triangles 6
Example 1 B
3.4cm
9.4cm
A
Q
10cm
C
3.4cm
9.4cm
10cm
R
P
AB = PQ (Corresponding Sides)
BC = QR (Corresponding Sides)
AC = PR (Corresponding Sides)
Therefore Congruent by SSS
7
Congruent Triangles 7
Example 2 B
9.4cm
Q
3.4cm
9.4cm
C
A
3.4cm
R
P
AB = PQ (Corresponding Sides)
BC = QR (Corresponding Sides)
B = Q (Included angle)
Therefore Congruent by SAS
8
Congruent Triangles 8
Example 3 B
A
20o
70o
10cm
Q
C
20o
70o
10cm
P
A = P (Corresponding Angles)
C = R (Corresponding Angles)
AC = PR (Corresponding Sides)
R
Therefore Congruent by AAS
9
Congruent Triangles 9
Example 4 B
A
Q
3.4cm
3.4cm
C
R
10cm
P
B = Q = 90o (Right Angle)
AC = PR (Hypotenuse)
BC = QR (Corresponding Sides)
10cm
Therefore Congruent by RHS
10