Class 8 Kites and Trapeziums — practice questions with answers
Quadrilaterals · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. In Indian textbooks, a trapezium is a quadrilateral with:
AAll sides equal
BNo parallel sides
CExactly two pairs of parallel sides
DAt least one pair of parallel sides
Show answer
Answer: D) At least one pair of parallel sides
A trapezium has at least one pair of parallel sides. By this inclusive definition, parallelograms also count as trapeziums.
2. Which property is NOT always true for a kite?
AThe diagonals are perpendicular
BOne pair of opposite angles is equal
CThe diagonals bisect each other
DIt has two pairs of equal adjacent sides
Show answer
Answer: C) The diagonals bisect each other
Only one diagonal is bisected in a kite. If both diagonals bisected each other, the shape would be a parallelogram (a rhombus).
3. In kite ABCD (AB = AD, CB = CD), ∠A = 70° and ∠C = 50°. Find ∠B.
A60°
B240°
C120°
D110°
Show answer
Answer: C) 120°
∠B = ∠D and all four add to 360°: 2∠B = 360° − 70° − 50° = 240°, so ∠B = 120°. 240° forgets to halve.
4. Where is the line of symmetry of an isosceles trapezium?
AThrough the midpoints of the two legs
BAlong one of its diagonals
CThrough the midpoints of the two parallel sides
DIt has no line of symmetry
Show answer
Answer: C) Through the midpoints of the two parallel sides
Folding along the line through the midpoints of the parallel sides makes the equal legs and equal base angles match.
5. In trapezium ABCD, AB ∥ DC and AD = DC. If ∠DAB = 76°, find ∠DCA.
A76°
B52°
C38°
D104°
Show answer
Answer: C) 38°
Triangle ADC is isosceles (AD = DC), so ∠DAC = ∠DCA. Also ∠DCA = ∠CAB (alternate angles). So AC splits ∠DAB into two equal parts: ∠DCA = 76° ÷ 2 = 38°.