Advertisements
Advertisements
प्रश्न
The figure, given below, shows a trapezium ABCD. M and N are the mid-point of the non-parallel sides AD and BC respectively. Find:
- MN, if AB = 11 cm and DC = 8 cm.
- AB, if DC = 20 cm and MN = 27 cm.
- DC, if MN = 15 cm and AB = 23 cm.
Advertisements
उत्तर
Let we draw a diagonal AC as shown in the figure below,
(i) Given that AB = 11 cm, CD = 8 cm
From triangle ABC
ON = `[1]/[2]` AB
= `[1]/[2]` × 11
= 5.5 cm
From triangle ACD
OM = `[1]/[2]` CD
=`[1]/[2]` × 8
= 4 cm
Hence, MN = OM + ON
= (4 + 5.5)
= 9.5 cm
(ii) Given that CD = 20 cm, MN = 27 cm
From triangle ACD
OM = `[1]/[2]` CD
= `[1]/[2]` × 20
= 10 cm
Therefore, ON = 27 - 10 = 17 cm
From triangle ABC
AB = 2ON
= 2 × 17
= 34 cm
(iii) Given that AB = 23 cm, MN = 15 cm
From triangle ABC
ON =`[1]/[2]` AB
=`[1]/[2]` × 23
= 11.5 cm
OM = 15 - 11.5
OM = 3.5 cm
From triangle ACD
CD = 2OM
= 2 × 3.5
CD = 7 cm
APPEARS IN
संबंधित प्रश्न
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
- D is the mid-point of AC
- MD ⊥ AC
- CM = MA = `1/2AB`
In the given figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of ΔABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.
In the given figure, seg PD is a median of ΔPQR. Point T is the mid point of seg PD. Produced QT intersects PR at M. Show that `"PM"/"PR" = 1/3`.
[Hint: DN || QM]
A parallelogram ABCD has P the mid-point of Dc and Q a point of Ac such that
CQ = `[1]/[4]`AC. PQ produced meets BC at R.
Prove that
(i)R is the midpoint of BC
(ii) PR = `[1]/[2]` DB
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 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 ΔABC, X is the mid-point of AB, and Y is the mid-point of AC. BY and CX are produced and meet the straight line through A parallel to BC at P and Q respectively. Prove AP = AQ.
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"`.
P and Q are the mid-points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.
