Class 9 Conditions for a Parallelogram — practice questions with answers
Geometry — Quadrilaterals · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. A quadrilateral is a parallelogram if both pairs of its opposite sides are:
Aequal
Bperpendicular
Cunequal
Dparallel only on one pair
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Answer: A) equal
If both pairs of opposite sides of a quadrilateral are equal, it is a parallelogram.
2. Which of the following is the converse used: 'In a quadrilateral, if each diagonal divides it into two congruent triangles, then it is a parallelogram'?
AA valid condition for a parallelogram
BA condition only for a rectangle
CNever true
DA condition only for a kite
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Answer: A) A valid condition for a parallelogram
If a diagonal divides a quadrilateral into two congruent triangles in this manner, opposite sides become equal, giving a parallelogram.
3. Which one is a property AND a defining condition for a parallelogram?
ADiagonals bisect each other
BDiagonals are perpendicular
CDiagonals are equal
DDiagonals are unequal
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Answer: A) Diagonals bisect each other
In a parallelogram diagonals bisect each other, and conversely this bisection proves a parallelogram.
4. In parallelogram ABCD, angle A = (3x + 10) deg and angle B = (2x - 30) deg. Using the adjacent-angle property, find the value of x.
A80
B36
C44
D40
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Answer: D) 40
Adjacent angles are supplementary: (3x + 10) + (2x - 30) = 180, so 5x - 20 = 180, 5x = 200, x = 40.
5. ABCD is a parallelogram. On side AB a point E is taken and on side DC a point F is taken such that AE = CF. Prove-style question: when AECF is formed (vertices A, E, C, F in order), it is a parallelogram because:
AAE is equal and parallel to CF
BAE = EC
CAC is perpendicular to EF
Dangle AEC = 90 deg
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Answer: A) AE is equal and parallel to CF
AE lies on AB and CF lies on DC; AB is parallel to DC, so AE is parallel to CF, and it is given AE = CF. One pair of opposite sides equal and parallel makes AECF a parallelogram.