Page 36 - Mathematics_Form_Two

Congruence

Example 2�9 2. Given that X and Y are the feet of the
In the following figure, prove that perpendiculars from B and C to AD

∆RVS ≅ ∆TVU. as shown in the following figure.
Prove that BX CY.=

FOR ONLINE READING ONLY
Mathematics for Secondary Schools 3. Line segments CB and AD intersect

at O such that AO =
OD. If AB is
parallel to CD, prove that AB CD.=
Solution

Given that RS// UT and RS UT= . 4. Consider the following figure.
Required to prove that ∆RVS ≅ ∆TVU.

Proof: In RVS∆ and TVU;∆ , it implies
that
)
ˆ
ˆ (alternate angles, RSes,l
SRV=UTV( Alternate ang // U T).
RS UT= (given) Prove that,
ˆ
ˆ
RSV=TUV (alternate angles, RSes,l // U T) )
( Alternate ang
(a) AO = OD (b) CO = OB
Therefore,
∆RVS ≅ ∆TVU (by ASA postulate). 5. In PQR, X is the midpoint of PQ,
Y and Z are the midpoints of PR
Exercise 2�4 and QR, respectively. If XYRZ is a

1. In the following figure, AC parallelogram, prove that XY = QZ.
ˆ
ˆ
bisects BAD and BCD, prove that 6. In the following figure, AB = AC.
AB AD.= Prove that BF = CE.

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Student's Book Form Two

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