Class 8 Constructing Quadrilaterals — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. How many independent measurements are needed to construct a unique quadrilateral?
A3
B4
C5
D6
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Answer: C) 5
A quadrilateral has 4 sides, 4 angles and 2 diagonals (10 elements). Out of these, exactly 5 measurements are required to draw a unique quadrilateral.
2. A rhombus can be constructed uniquely from:
Aits perimeter only
Bits two diagonals
Cone side only
Done angle only
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Answer: B) its two diagonals
The diagonals of a rhombus bisect each other at right angles. Knowing both diagonals fixes the four vertices, giving a unique rhombus.
3. The last vertex of a quadrilateral, when 4 sides and 1 diagonal are given, is found by:
Ameasuring an angle with protractor
Bthe intersection of two arcs of the remaining two sides
Cextending the diagonal
Djoining the two known vertices
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Answer: B) the intersection of two arcs of the remaining two sides
After the first triangle is drawn, the fourth vertex lies where arcs of the two remaining side lengths (from the two appropriate vertices) cross.
4. A rectangular notebook cover is to be constructed with length 18 cm and breadth 12 cm. The diagonal of this rectangle, needed to check the construction, is:
A613 cm
B30 cm
C30 cm
D15 cm
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Answer: A) 613 cm
Diagonal = 182+122=324+144=468=36×13=613 cm.
5. An architect must lay out a parallelogram-shaped hall ABCD with AB = 10 m, BC = 6 m and the longer diagonal AC = 16 m. Using the parallelogram law, the diagonals satisfy AC² + BD² = 2(AB² + BC²). Find the shorter diagonal BD (in metres).