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

Prove that :
(i) DE is parallel to FB
(ii) DE = FB
(iii) DEBF is a parallelogram

The following figure shows a trapezium ABCD in which AB is parallel to DC and AD= BC Prove that: angleDAB= angleCBA

The following figure shows a trapezium ABCD in which AB is parallel to DC and AD= BC Prove that: OA = OB and OC= OD

The following figure shows a trapezium ABCD in which AB is parallel to DC and AD= BC Prove that: angleADC= angleBCD

The adjoining figure shows a parallelogram ABCD in which P is mid-point of AB and Q is mid-point of CD. Prove that AE=EF=FC .

The given figure shows a rectangle ABDC and a parallelogram ABEF, drawn on opposite sides of AB. Prove that : (i) quadrilateral CDEF is a parallelogram, (ii) Area of quad. CDEF = Area of rec. ABDC + "Area of" ////gm.ABEF .

The following figure shows a trapezium ABCD in which AB is parallel to DC and AD = BC. Prove that : (i) angleDAB=angleCBA (ii) angleADC=angleBCD (iii) AC = BD (iv) OA = OB and OC = OD

In the adjoining figure ABCD is a parallelogram, ABM is a line segment and E is the mid-point of BC. Prove that : (i) DeltaDCE cong DeltaMBe (ii) AB = BM (iii) AM=2DC

The given figure shows parallelogram ABCD. Points M and N lie in diagonal BD such that DM=BN . Prove that: (i) DeltaDMCcong DeltaBNA and so CM=AN. (ii) DeltaAMDcongDeltaCNB and so AM=CN . (iii) ANCM is a parallelogram.

In the given figure, ABCD is a parallelogram in which AN and CP are perpendiculars on diagonal BD. Prove that : (i) DeltaADN =DeltaCBP (ii) AN=CP

In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that: (i) AX=YC. (ii) AX is parallel to YC (iii) AXCY is a parallelogram.