Mathematics
In the given figure, ABCD is a square, EF || BD and R is the mid-point of EF. Prove that:
(i) BE = DF
(ii) AR bisects ∠BAD
(iii) If AR is produced, it will pass through C.
Related Questions
Equilateral triangle ABD and ACE are drawn on the sides AB and AC of △ABC as shown in the figure. Prove that :
(i) ∠DAC = ∠EAB
(ii) DC = BE
In the given figure, ABCD is a square and P, Q, R are points on AB, BC and CD respectively such that AP = BQ = CR and ∠PQR = 90°. Prove that:
(i) PB = QC
(ii) PQ = QR
(iii) ∠QPR = 45°
ABCD is a parallelogram in which ∠A and ∠C are obtuse. Points X and Y are taken on diagonal BD such that ∠AXD = ∠CYB = 90°. Prove that : XA = YC.
ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively such that AB = BE and AD = DF. Prove that △BEC ≅ △DCF.
