Page 30 - Mathematics_Form_Two

Congruence

From Figure 2.2, it follows that BC = AD (given)
AB PQ= (given)
AC AC= is a common side to both triangles.
BC QR= (given)
Therefore, ABC  CDA (By SSS).
AC PR= (given)
ˆ
ˆ
Hence BAC = DCA

CDA, hence deduce that READING ONLY
Since the pairs of the corresponding sides
(definition of congruent triangles).
Mathematics for Secondary Schools the two triangles are exactly the same. Example 2�5
of triangles ABC and PQR are equal, then
Therefore, it follows that,
PQR (by SSS).
ABC 

Triangle ABC is an isosceles triangle
in which AB and AC are equal. If
Since the two triangles are congruent, it
implies that, their corresponding angles
ACD.

ABD 
are also equal, that is, D is the midpoint of BC, prove that
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ RPQ, ABC = PQR and BCA = QRP. Solution
CAB =
Consider the ABC such that AB AC=
Example 2�4 and D is a mid-point of BC. as shown in
the following figure.
Use the following figure to prove that
FOR ONLINE
 ABC 
ˆ
ˆ
DCA = BAC.

Required to prove that ABD  ACD.
Construction: Use a dotted line to join
the points A andD.

Proof: In ABD ABD and ACD.ACD.

Solution
Given, a rectangle ABCD in which AB AC= (given)
AB = DC, and AD = BC . BD DC= (given)

Construct a line joining A and C. AD AD= is a common side to both triangles.
Proof: From ABC∆ and CDA∆ Therefore,

AB = DC (given)  ABD  ACD. (by SSS).

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Student's Book Form Two

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