1 SMART EDUCATIONS ( www.smarteducations.org )
QUADRILATERALS
1. Opposite angles of a parallelogram are …………
2. In a parallelogram, if one angle measure 115
o
, find the other angles.
3. The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the
length of each side of the rhombus.
4. State and prove Mid Point Theorem.
5. A parallelogram has one angle measure 90
0
. Find rest three angles of it
6. If the sides of a parallelogram are 8cm and 6cm, find the diagonals.
7. Write two properties of a parallelogram.
8. Sum of adjacent angles of a square is
9. Show that the bisectors of angles of parallelogram form a rectangle.
10. State and prove Converse of Mid Point Theorem.
11. Show that A diagonal of a parallelogram divides it into two congruent triangles.
12. Show that In a parallelogram, opposite sides are equal.
13. Show that If each pair of opposite sides of a quadrilateral is equal, then it is a
parallelogram.
14. Show that The diagonals of a parallelogram bisect each other.
15. Show that If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
16. Show that each angle of a rectangle is a right angle.
17. Show that the diagonals of a rhombus are perpendicular to each other.
18. : Show that A quadrilateral is a parallelogram if a pair of opposite sides is equal and
parallel.
19. ABCD is a rhombus. Show that diagonal AC bisects ∠ A as well as ∠ C and diagonal BD
bisects ∠ B as well as ∠ D.
20. ABCD is a trapezium in which AB || CD and AD = BC. Show that (i) ∠ A = ∠ B (ii) ∠ C =
∠ D (iii) ∆ ABC ≅ ∆ BAD
21. ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: (i)
ABCD is a square (ii) diagonal BD bisects ∠ B as well as ∠ D.
22. ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse AB and
parallel to BC intersects AC at D. Show that (i) D is the midpoint of AC (ii) MD ⊥AC (iii)
CM = MA = AB.
1
2
23. ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the midpoint of AD. A
line is drawn through E parallel to AB intersecting BC at F. Show that F is the midpoint of
BC.
