Question

D and F are mid-points of sides AB and AC of a triangle ABC. A line through
F and parallel to AB meets BC at point E.
(1) Prove that BDFE is a parallelogram.
(1) Find AB, if EF = 5.2 cm.​

Answer 1

Answer: Pls mark as brainliest

Step-by-step explanation:

consider ΔABC

E and F are midpoints of the sides AB and AC

The line joining the midpoints of two sides of a triangle is parallel to the third side and half the third side

⇒ EF || BC

⇒ EF || BD …(i)

And EF =  × BC

But D is the midpoint of BC therefore  × BC = BD

⇒ EF = BD …(ii)

E and D are midpoints of the sides AC and BC

⇒ ED || AB

⇒ ED || FB …(iii)

And ED =  × AB

But F is the midpoint of AB therefore  × AB = FB

⇒ ED = FB …(iv)

Using (i), (ii), (iii) and (iv) we can say that BDEF is a parallelogram

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Answer 2

(2) AB=10.4 cm

Step-by-step explanation:

In triangle ABC

D is a mid-point of side AB

F is a mid-point of side AC

By mid-segment theorem

DF is parallel to BC and

$DF=\frac{1}{2}BC$

FE is parallel to AB and F is a mid-point of side AC

By converse of mid-segment theorem

E is a mid-point of BC

BE=EC

DF=BE

DF is parallel to BC therefore, DF is parallel to BE

FE is parallel to AB.Therefore, FE is parallel to DB

When pair of opposite sides are parallel then the quadrilateral is a parallelogram.

Hence, BDEF is a parallelogram.

(2)By mid-segment theorem

$EF=\frac{1}{2}AB$

$AB=2EF=2(5.2)=10.4 cm$

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