ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF =
A. 3/2 AB
B. 2 AB
C. 3 AB
D. 5/4 AB
Answers
Given : ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F.
To find : The value of AF
Proof :
In ∆CED & ∆BEF ,
∠BEF = ∠CED
[vertically opposite angles]
BE = CE
[E is the mid-point of BC]
∠EDC = ∠EFB
[ alternate angles]
∴ ∆ECD ≅ ∆BEF
[By AAS congruence criterion]
So, CD = BF ………….(1)
[By CPCT]
∵ ABCD is a parallelogram , i.e , AB = CD ………(2)
Thus, AF = AB + BF
AF = AB + CD
[From eq 1]
AF = AB + AB
[From eq 2]
AF = 2AB
Hence, the value of AF is 2AB.
Among the given options option (B) 2AB is correct.
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Answer:-
Given :
ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F.
To find :
The value of AF
Proof :
In ∆CED & ∆BEF ,
∠BEF = ∠CED
[vertically opposite angles]
BE = CE
[E is the mid-point of BC]
∠EDC = ∠EFB
[ alternate angles]
∴ ∆ECD ≅ ∆BEF
[By AAS congruence criterion]
So, CD = BF ………….(1)
[By CPCT]
∵ ABCD is a parallelogram , i.e , AB = CD ………(2)
Thus, AF = AB + BF
AF = AB + CD
[From eq 1]
AF = AB + AB
[From eq 2]
AF = 2AB
Hence, the value of AF is 2AB.
Among the given options option (B) 2AB is correct.
Hope it's help you❤️