Advertisements
Advertisements
प्रश्न
Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Advertisements
उत्तर
Join AC.
P and Q are mid-points of AB and BC respectively.
∴ PQ || AC, PQ = `(1)/(2)"AC"`.........(i)
S and R are mid-points of AD and DC respectively.
∴ SR || AC, SR = `(1)/(2)"AC"`.........(ii)
From (i) and (ii)
PQ = SR
Therefore, PQRS is a parallelogram.
Since, diagonals of a parallelogram bisect each other
Therefore, PQ and QS bisect each other.
APPEARS IN
संबंधित प्रश्न
In the Figure, `square`ABCD is a trapezium. AB || DC. Points P and Q are midpoints of seg AD and seg BC respectively. Then prove that, PQ || AB and PQ = `1/2 ("AB" + "DC")`.
Use the following figure to find:
(i) BC, if AB = 7.2 cm.
(ii) GE, if FE = 4 cm.
(iii) AE, if BD = 4.1 cm
(iv) DF, if CG = 11 cm.
In trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC.
Prove that: AB + DC = 2EF.
In the given figure, AD and CE are medians and DF // CE.
Prove that: FB = `1/4` AB.
In triangle ABC, D and E are points on side AB such that AD = DE = EB. Through D and E, lines are drawn parallel to BC which meet side AC at points F and G respectively. Through F and G, lines are drawn parallel to AB which meets side BC at points M and N respectively. Prove that: BM = MN = NC.
The diagonals of a quadrilateral intersect each other at right angle. Prove that the figure obtained by joining the mid-points of the adjacent sides of the quadrilateral is a rectangle.
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.
In the given figure, ABCD is a trapezium. P and Q are the midpoints of non-parallel side AD and BC respectively. Find: AB, if DC = 8 cm and PQ = 9.5 cm
In the given figure, T is the midpoint of QR. Side PR of ΔPQR is extended to S such that R divides PS in the ratio 2:1. TV and WR are drawn parallel to PQ. Prove that T divides SU in the ratio 2:1 and WR = `(1)/(4)"PQ"`.
The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is ______.
