Mathematics
In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that :
(i) AE = AD
(ii) DE bisects angle ADC
(iii) angle DEC is a right angle
Related Questions
In the following figure, ABCD and PQRS are two parallelograms such that ∠D = 120° and ∠Q = 70°. Find the value of x.
In the following figure, ABCD is a rhombus and DCFE is a square.
If ∠ABC = 56°, find :
(i) ∠DAE
(ii) ∠FEA
(iii) ∠EAC
(iv) ∠AEC
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
Prashant had a plot of land in the shape of a quadrilateral. He constructed his house in the middle by joining the mid-points of the four sides of the land and used the remaining four portions at the four ends for different purposes, like a small garden, swimming pool, etc.
(i) What type of a quadrilateral is PQRS ?
(ii) What are the lengths of adjacent sides of the quadrilateral PQRS, if their ratio is 1 : 2 and the perimeter of the quadrilateral is 180 m ?
(iii) In quadrilateral PQRS, if ∠PSQ = 30° and ∠QRS = 110°, find ∠SQP.