Mathematics
In the given figure, ABCD is a parallelogram, E is a point on BC and the diagonal BD intersects AE at F.
Prove that DF × FE = FB × FA.
Related Questions
In the given figure, AC ∥ DE ∥ BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm, BF = 30 cm.
(i) Prove that ΔGED ∼ ΔGBF.
(ii) Find DE.
(iii) Find DB : AB.
In the adjoining figure, ABCD is a parallelogram, P is a point on side BC and DP when produced meets AB produced at L. Prove that :
(i) DP : PL = DC : BL.
(ii) DL : DP = AL : DC.
In the adjoining figure (not drawn to scale), PS = 4 cm, SR = 2 cm, PT = 3 cm and QT = 5 cm.
(i) Show that ΔPQR ∼ ΔPST.
(ii) Calculate ST, if QR = 5.8 cm.
In the adjoining figure, ABCD is a parallelogram in which AB = 16 cm, BC = 10 cm and L is a point on AC such that CL : LA = 2 : 3. If BL produced meets CD at M and AD produced at N, prove that :
(i) ΔCLB ∼ ΔALN.
(ii) ΔCLM ∼ ΔALB.
