Which construction step is crucial when constructing a rhombus given its diagonals?

Constructing perpendicular bisectors

Drawing diagonals of equal length

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 diagonal and side lengths to form two triangles

Using the side lengths to form two triangles

Constructing perpendicular bisectors

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.

This ICSE Class 9 Mathematics practice quiz has 45 multiple-choice questions on Construction of Quadrilaterals & Polygons, and 45 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Sample questions

In a quadrilateral ABCD, if angle A = 100°, angle B = 80°, angle C = 70°, what is the measure of angle D?
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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:
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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?
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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?
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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:
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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.

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More questions in this quiz

Answers and explanations are in the full quiz.

Which of the following quadrilaterals has diagonals that are perpendicular bisectors of each other?
What is the sum of the interior angles of a regular polygon with 9 sides?
A square has a perimeter of 48 cm. What is its area?
If the diagonals of a quadrilateral bisect each other, what type of quadrilateral must it be?
What is the measure of each interior angle of a regular hexagon?
In a trapezoid ABCD, AB is parallel to CD. If AD = BC and angle A = 60°, what is angle B?
A rhombus has diagonals of length 12 cm and 16 cm. What is the length of each side?
In a cyclic quadrilateral ABCD, angle A = 85°, what is angle C?
To construct a square, you need to know:
Which of the following statements is NOT always true for a rectangle?
If a pentagon is regular, how many degrees is each exterior angle?
To construct a parallelogram given two adjacent sides and the angle between them, you need:
A quadrilateral ABCD has angles A = 90°, B = 90°, C = 120°. What is angle D?
If a quadrilateral has all sides equal and all angles equal, it is a:
The sum of the interior angles of a regular decagon (10 sides) is:
In an isosceles trapezoid, the non-parallel sides are equal. What is true about its base angles?
A parallelogram has sides of length 5 cm and 7 cm. If the perimeter is 24 cm, what are the lengths of the sides?
What is the sum of the interior angles of a polygon with 12 sides?
To construct a kite, you generally need to know:
If a quadrilateral has diagonals that are equal and bisect each other, it must be a:
A regular heptagon has how many degrees in each interior angle?
Which type of quadrilateral is formed by joining the midpoints of the sides of a rhombus?
To construct a rectangle, you need to know:
If the sum of two opposite angles of a quadrilateral is 180°, and the sum of the other two opposite angles is also 180°, what can you conclude?
To construct a square with a side length of 5 cm, what is the essential angle to construct?
Which of the following statements is true for all parallelograms?
What is the sum of the interior angles of a regular octagon (8 sides)?
When constructing a quadrilateral with three sides and two included angles given, which angle is typically constructed first after drawing one of the given sides?
If a quadrilateral is a rhombus, which of these is true?
A quadrilateral ABCD is inscribed in a circle such that AB is parallel to DC. What type of quadrilateral is it?
In a parallelogram ABCD, if angle A = 75°, what is the measure of angle B?
What is the sum of the exterior angles of a regular polygon with 15 sides?
In a kite, if one diagonal bisects the angles at the vertices it joins, what else must be true about that diagonal?
Which property is NOT shared by both a square and a rhombus?
What is the sum of the interior angles of a convex polygon with 7 sides?
To construct a square with a given diagonal length 'd', you would first construct:
If a quadrilateral has diagonals that bisect each other at right angles, it is a:
What is the measure of each interior angle of a regular dodecagon (12 sides)?
To construct a trapezoid when three sides and one angle are given, it is often necessary to:
What is the minimum number of independent conditions required to define a unique rectangle?

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