Quadrilaterals-Important Questions

1.   If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a parallelogram.

2.   L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD, prove that DL, DK, BM and BN enclose a rhombus.

3.   PQRS is a parallelogram. PS is produced to meet M so that SM = SR and MR is produced to meet PQ produced at N. Prove that QN= QR.

4.   In a ΔABC, DE is parallel to BC and D is the mid-point of side AB. Find the perimeter of ΔABC when AE = 4.5 cm, DE = 5 cm and DB = 3.5 cm.

5.   If an angle of a parallelogram is 4/5 of it adjacent angle, then find the measures of all the angles of the parallelogram.

6.   ABCD is a trapezium in which AB is parallel to CD. If ∟A = 36° and ∟B = 81°, then find ∟C and ∟D.

7.   In a ΔABC, DE is parallel to BC and D is the mid-point of side AB. Find AE and BC if DE = 6 cm and EC = 5 cm.

8.   In a parallelogram ABCD find the measure of all the angles if one angle measures 68°.

9.   The lengths of diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

10.   In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice the smallest angle.