Advertisements
Advertisements
प्रश्न
In ΔABC, D and E are the midpoints of the sides AB and AC respectively. F is any point on the side BC. If DE intersects AF at P show that DP = PE.
उत्तर
Note: This question is incomplete.
According to the information given in the question,
F could be any point on BC as shown below:
So, this makes it impossible to prove that DP = DE, since P too would shift as F shift because P too would be any point on DE as F is.
Note: If we are given F to be the mid-point of BC, the result can be proved.
D and E are the mid-points of AB and AC respectively.
DE || BC and DE = `(1)/(2)"BC"`
But F is the mid-point of BC.
⇒ BF = FC = `(1)/(2)"BC"` = DE
Since D is the mid-point of AB, and DP || EF, P is the mid-point of AF.
Since P is the mid-point of AF and E is the mid-point of AC,
PE = `(1)/(2)"FC"`
Also, D and P are the mid-points of AB and AF respectively.
⇒ DP = `(1)/(2)"BF"`
= `(1)/(2)"FC"`
= PE ....(Since BF = FC)
⇒ DP = PE.
APPEARS IN
संबंधित प्रश्न
In below fig. ABCD is a parallelogram and E is the mid-point of side B If DE and AB when produced meet at F, prove that AF = 2AB.
ABCD is a kite having AB = AD and BC = CD. Prove that the figure formed by joining the
mid-points of the sides, in order, is a rectangle.
In below Fig, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such that CQ = `1/4` AC. If PQ produced meets BC at R, prove that R is a mid-point of BC.
In the given figure, M is mid-point of AB and DE, whereas N is mid-point of BC and DF.
Show that: EF = AC.
In ΔABC, AB = 12 cm and AC = 9 cm. If M is the mid-point of AB and a straight line through M parallel to AC cuts BC in N, what is the length of MN?
In a parallelogram ABCD, M is the mid-point AC. X and Y are the points on AB and DC respectively such that AX = CY. Prove that:
(i) Triangle AXM is congruent to triangle CYM, and
(ii) XMY is a straight line.
ABCD is a parallelogram.E is the mid-point of CD and P is a point on AC such that PC = `(1)/(4)"AC"`. EP produced meets BC at F. Prove that: F is the mid-point of BC.
In the given figure, PS = 3RS. M is the midpoint of QR. If TR || MN || QP, then prove that:
RT = `(1)/(3)"PQ"`
D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively, then DEQP is ______.
E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = `1/3` AC.
