E is the Mid-point of Side Ab and F is the Mid-point of Side Dc of Parallelogram Abcd. Prove that Aefd is a Parallelogram

E is the mid-point of side AB and F is the mid-point of side DC of parallelogram ABCD. Prove that AEFD is a parallelogram.

Sum

Let us draw a parallelogram ABCD Where F is the midpoint Of side DC and E is the mid-point of side AB of a parallelogram ABCD.

To prove: AEFD is a parallelogram

Proof:
In parallelogram ABCD
AB || DC
BC || AD
AB = DC
`1 /2"AB" = 1/2`DC
AE = DF
Also AD || EF
Therefore, AEFD is a parallelogram.

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Chapter 13 Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Exercise 14 (C) | Q 1 | Page 181

The alongside figure shows a parallelogram ABCD in which AE = EF = FC.

Prove that:

In the alongside diagram, ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B.

Prove that:

In the given figure, ABCD is a parallelogram.

Prove that: AB = 2 BC.

Prove that the bisectors of opposite angles of a parallelogram are parallel.

Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN. Prove that BMDN is a parallelogram.

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: ∠RTS = 90°

ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.

Prove that: BP bisects ∠ABC.

In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that: BC = BE.

Which of the following statement is correct?

Construct a parallelogram POUR in which, PO = 5.5 cm, OU = 7.2 cm and ∠O = 70°.