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Question

In the given figure, ABCD is a quadrilateral with 1=2 and 3=ABC and 4=BAD. Also, AP and BQ are produced to points E and F, respectively. Then, we can say that

A
ΔOFE is an equilateral triangle
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B
ΔOFE is an isosceles triangle
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C
ΔOFE is a scalene triangle
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D
Can't be determined
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Solution

The correct option is B ΔOFE is an isosceles triangle
Given, ABCD is a quadrilateral with 1=2,3=ABC and 4=BAD
In ΔAPB and ΔEPC,
APB=CPE [vertically opposite angles]
PCE=3=PBA [given]
ΔAPBΔEPC [by AA similarity]
PEC=1 ...(i)
Similarly, in ΔFQD and ΔBQA,
QFD=2 ...(ii)
From Eqs. (i) and (ii), we get
PEC=QFD [1=2, given]
OFE=OEF
OF=OE
ΔOFE is an isosceles triangle.

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