Question

In Figure ABCD is a parallelogram and E is the  mid-point of side BC. If DE and AB when  produced meet at F, then AF÷AB =​

Answer 1

Answer:

answer for the given problem is given

Answer 2

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GiveN:

• ABCD is a parallelogram.
• E is the mid-point of side BC.
• DE and AB is produced meet at F.

To FinD:

• AF / AB = ?

Step-wise-Step Explanation

In parallelogram ABCD, AB || DC ⇒ AF || DC

Then, ∠CDF = ∠DFB

E is the midpoint of side BC

Then, CE = BE

In ∆DEC and ∆BEF,

• CE = BE
• ∠CDF = ∠DFB
• ∠CEB = ∠BEF ( Vertically opposite)

⇒ ∆DEC ≅ ∆BEF (By AAS congurence)

They means, DC = BF (CPCT)

⇒ AB = BF (opposite sides are equal)

We need to find: AF / AB

⇒ AB + BF / AB

⇒ 2AB / AB (Determined above)

⇒ 2 (Answer)

Hence,

• The required value of ratio AF / AB is 2.