Page 32 - Mathematics_Form_Two

Congruence

11. Use the following figure to find the (given)
ˆ
measure of ABD.
Therefore, ABC D @D (by SAS).
PRQ
Since the two triangles are congruent, it
follows that, all the corresponding sides
and angles are equal. ˆ ˆ
FOR ONLINE READING ONLY
Mathematics for Secondary Schools Side-Angle-Side (SAS) postulate Example 2�6
ˆ
ˆ
That is, BAC= QPR, ABC=PRO, and
AB = PR.

Two triangles are congruent if two pairs of
their corresponding sides and the angles
Use the following figure to prove that
included between the two sides are equal.
Figure 2.3 illustrates the postulate. ΔADC ≅ ΔCBA.

Solution
Required to prove that,
CBA.
 ADC 
Proof: From ADC and CBA, , it
follows that

DC = AB (given)
ˆ
ˆ
DCA = BAC (given)
Figure 2�3: Pair of congruent triangles AC AC= is a common side to both triangles.
satisfying SAS postulate
Therefore,
From Figure 2.3, AC and PQ, and BC ΔADC ≅ ΔCBA (by SAS).
and RQ are two pairs of corresponding
ˆ
ˆ
sides while ABC and PQR is a pair of
corresponding angles. It follows that, Example 2�7
AC = PQ (given) Use the following figure to prove that
ˆ
ˆ
BCA = RQP (given) AD CD.=

26
Student's Book Form Two

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MATHEMATIC F2 v5.indd 26 11/10/2024 20:11:17