Page 33 - Mathematics_Form_Two

Congruence

In Figure 2.4 AB C∆ 1 and AB C,∆ 2 have
CB
4 cm.
two pairs of equal sides (CB = ,and CB= 2 2 4 cm.
CB = = ) and
1 1
ˆ
one pair of equal angles (CAB = ). However,
30 ,°
1
SAS postulate cannot be used because
angle CAB is not included between the
1
FOR ONLINE READING ONLY
CB
CB = .
two equal sides CB = , and CB= 4 cm.m.= 4 c
1 1 2 2
Solution Exercise 2�3
Given ABC such that BA = BC and 1. In the following figure, AO OD=AO OD=
ˆ
ˆ
ABD = DBC, . and OB OC.=OB OC.= Mathematics for Secondary Schools
(a) Prove that AB = CD.
DC
Required to prove that AD = DC.
(b) Write the angle which is equal
Proof: In ABD and CBD  , it implies to ABO.
ˆ
OAB.
that
BA = BC (given)
ˆ
ˆ
ABD = CBD (given)
BD = is a common side.
BD
Thus, ABD  CBD (by SAS)
Since the two triangles are congruent, 2. In the following figure, if AB = DC
ˆ
ˆ
it follows that all sides and angles are and ABC = DCB, prove that
equal. AC= DB.

Therefore, AD = CD .

Note that, two triangles may have two
equal sides and angles but not qualify to
be congruent. This is described in AB C∆ 1
and AB C∆ in Figure 2.4.
2
3. In the following figure, if AX= DX
and prove that

ˆ
ˆ
BAC = CDB.

Figure 2�4: Demonstrating non-congruence of
triangles

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Student's Book Form Two

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