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pranjal abhishek

· started a discussion

· 1 Months ago

AX||CY (Question:96558.0)

If two sides are parallel then it must be trapezium. so option b is correct and a also

Question:
In the given figure, ABCD is a parallelogram and line segments AX, CY bisect the angles A and C respectively, then which one is true :


Options:
A) AX ∥ CY
B) AXCY is a trapezium
C) AX is not parallel to CY
D) None of these.
Solution:

ABCD is ∥ gm (given)

∴ ∠A = ∠C

⇒ \(\cfrac{1}{2}\) ∠A  =  \(\cfrac{1}{2}\) ∠C

⇒ ∠1 = ∠2         …(i)

Now, AB ∥DC and the transversal CY intersects then:

∴ ∠2 = ∠3          …(ii)

from (i) and (ii), we get ∠1 = ∠3.Thus, transversal AB intersects AX and YC at A and Y such that ∠1 = ∠3 i.e. corresponding angles are equal.

∴ AX ∥ CY.

Knowledge Expert

· commented

· 1 Months ago

Dear student,
Given answer is correct.
Keep learning,
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