Teach GCSE Maths Congruent Congruent Triangles Triangles
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Teach GCSE Maths
Congruent Congruent TrianglesTriangles
Teach GCSE Maths
Congruent Congruent TrianglesTriangles
© Christine Crisp
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Congruent triangles form just one type of congruent shapes.
However, they are very useful so it’s worth looking at them in more detail.
D
E
F
A
B
C
Congruent triangles have 3 pairs of equal sides.
Sides AC and DF are a pair of equal sides
The other pairs of equal sides are AB and DE,and BC and
EF.
Which angle forms a pair with A?
Which with B? And which with C?
D
E
F
A
B
C
ANS: The pairs are A and D, B and E, C and F
There are also 3 pairs of equal angles.
Sides AC and DF are a pair of equal sides
Congruent triangles have 3 pairs of equal sides.
D
E
F
A
B
C
There are also 3 pairs of equal angles.
Sides AC and DF are a pair of equal sides
We use a variety of symbols to mark angles. The same symbol in 2 or more angles means
they are equal.
Congruent triangles have 3 pairs of equal sides.
Equal sides are always opposite equal angles.e.g. If we are told that these triangles are
congruentP Q
S
A
C
B
and QS =
CA ( opposite the 90º angle )BA ( opposite the angle
with the cross )So, PQ = CB ( 3rd sides of the triangles
)
PS =
X
Y
Z
A
B
C
7
cm7
cm
Equal sides are always opposite equal angles.
XY = CA ( opposite )
X = C ( opposite the 7 cm sides)
So, XZ = BC ( 3rd sides )
So, Y = A ( 3rd angles )
e.g. If these are congruent
SUMMARY
Equal sides are always opposite equal angles.
Congruent triangles have 3 pairs of equal sides and 3 pairs of equal angles.
X
Y
Z
A
B
C
Triangle XYZ and CAB are congruent.
Exercise1. If these triangles are congruent,
which sides are equal? Give the reasons.A
BC
XY
Z
2. If these triangles are congruent, which angles are equal? Give the reasons.
A
B C
Y Z
X
6 cm
8 cm
6 cm
8 cm
Ans:
AC = ZY ( opposite )
So, AB = ZX ( 3rd sides )
BC = XY ( opposite )
1. If these triangles are congruent, which sides are equal? Give the reasons.
A
BC
XY
Z
Exercise
2. If these triangles are congruent, which angles are equal? Give the reasons.
A
B C
Y Z
X
C = X ( opposite the 6 cm sides )
6 cm
8 cm
6 cm
8 cm
A = Z ( opposite the 8 cm sides )
B = Y ( 3rd side of triangles )
Ans:
Suppose we put 2 right angled congruent triangles together like this:
We now have an isosceles triangle.We can reverse this, so any isosceles triangle can be made into 2 right angled congruent triangles.
e.g.
Since the triangles are congruent, these lengths . . .are equal.
The line must be drawn from the vertex where the equal sides meet, vertex A.
The perpendicular from A bisects the base.
A
We say that
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