Page 35 - Mathematics_Form_Two

Congruence

Figure 2.5 shows that, Consider triangles ABC and XZY in

BA = QP (given) Figure 2.6,
ˆ
ˆ
ABC = PQR (given) BAC = ZXY (given)
ˆ
ˆ

ˆ
ˆ
BCA = QRP (given) AC = XY (given)

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Thus, the two triangles satisfy the AAS ACB XYZ (given)
ˆ
ˆ
=
postulate.
Therefore ∆ABC ≅ ∆XYZ (by ASA
Therefore, ABC  PQR (by AAS). postulate).
Since the two triangles are congruent, it Mathematics for Secondary Schools
follows that, all corresponding sides and Example 2�8
angles are equal. That is, In the following figure, prove that
ˆ
ˆ
BA = QP, AC = PR, and BAC = QPR.
 ABC  CDA.
Similarly, if two angles and one included
side of the first triangle are equal to two
angles and an included side of the second
triangle, then the triangles are congruent
by Angle-Side-Angle (ASA) postulate as
described in Figure 2.6.

Solution
Given a parallelogram ABCD where
AC, is its diagonal.
Required to prove that,

 ABC  CDA.
Proof: In ABC and CDA  it follows
that,

ˆ
ˆ
CAB = ACD .
(alternate interior angles as AB / /DC ).

Similarly,
ˆ
ˆ
ACB = CAD
(alternate interior angles as AD / /BC ).

AC AC= is a common side.

Therefore, ABC  CDA (by AAS).
Figure 2�6: Triangles satsfying ASA postulate

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Student's Book Form Two

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