Construction of Quadrilaterals & Polygons Quiz - ICSE Class 9 Mathematics
Free practice quiz: Construction of Quadrilaterals & Polygons (ICSE Class 9 Mathematics). 45 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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In a quadrilateral ABCD, if angle A = 100°, angle B = 80°, angle C = 70°, what is the measure of angle D?
- 110°
- 90°
- 120°
- 100°
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Answer: A. 110°
The sum of interior angles of a quadrilateral is 360°. Therefore, angle D = 360° - (angle A + angle B + angle C) = 360° - (100° + 80° + 70°) = 360° - 250° = 110°.
The sum of exterior angles of any convex polygon is:
- 180°
- 360°
- Depends on the number of sides
- 0°
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Answer: B. 360°
The sum of the exterior angles of any convex polygon, one at each vertex, is always 360°.
Which construction step is crucial when constructing a rhombus given its diagonals?
- Bisecting the diagonals
- Constructing perpendicular bisectors
- Both A and B
- Drawing diagonals of equal length
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Answer: C. Both A and B
To construct a rhombus from its diagonals, you need to draw the diagonals, bisect them (they bisect each other at their midpoints), and ensure they are perpendicular. Therefore, both bisecting the diagonals and constructing perpendicular bisectors are crucial.
What is the angle between the diagonals of a square?
- 60°
- 90°
- 120°
- 180°
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Answer: B. 90°
The diagonals of a square are perpendicular bisectors of each other, so the angle between them is 90°.
If you are given the lengths of two adjacent sides of a rhombus and the length of one diagonal, you can construct it by:
- Using the side lengths to form two triangles
- Using the diagonal and side lengths to form two triangles
- Constructing perpendicular bisectors
- All of the above
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Answer: B. Using the diagonal and side lengths to form two triangles
A rhombus is composed of two congruent isosceles triangles (formed by a diagonal). If you know the diagonal and the side length (which is common to both triangles), you can construct these two triangles and join them along the diagonal to form the rhombus.