Which of the following is NOT sufficient information to construct a quadrilateral?

Two adjacent sides and three angles

Three angles and two included sides

Under what conditions is it impossible to construct a quadrilateral given the lengths of its four sides?

When the sum of lengths of any three sides is less than the fourth side

When the sum of lengths of any three sides is greater than the fourth side

When the sides form a rectangle

When the quadrilateral is cyclic

Quizzes / CBSE / Class 8 / Mathematics / Practical Geometry

Constructing Quadrilaterals Quiz - CBSE Class 8 Mathematics

Free practice quiz: Constructing Quadrilaterals (CBSE Class 8 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 11 multiple-choice questions on Constructing Quadrilaterals, and 11 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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Five measurements fix a quadrilateral

A general quadrilateral can be drawn uniquely when five suitable measurements are given.
NCERT cases: four sides and one diagonal; two diagonals and three sides; two adjacent sides and three angles.
Also: three sides and two included angles. Four sides alone are not enough because the shape can flex.

Common mistake: Thinking four sides are enough. Without a diagonal or an angle, many different quadrilaterals have the same four sides.

Angle sum property

The four interior angles of any quadrilateral always add up to 360°.
If given angles do not total 360°, such a quadrilateral cannot exist.

Angle sum

\[\angle A + \angle B + \angle C + \angle D = 360^\circ\]

Missing fourth angle

\[\angle D = 360^\circ - (\angle A + \angle B + \angle C)\]

Common mistake: Using 180°, the triangle angle sum, instead of 360° for a quadrilateral.

When four sides cannot work

Every side must be shorter than the sum of the other three sides.
If the longest side is equal to or greater than that sum, the sides cannot close up.

Condition (a is the longest side)

\[a < b + c + d\]

Common mistake: Testing a shorter side instead of the longest one. Always compare the longest side with the sum of the remaining three.

Special quadrilaterals need less data

Properties supply missing parts. A parallelogram has equal opposite sides and supplementary adjacent angles.
Parallelogram: two adjacent sides and the included angle. Rhombus: both diagonals, or one side and one angle.
Rectangle: two adjacent sides. Square: one side only.

Adjacent angles of a parallelogram

\[\angle A + \angle B = 180^\circ\]

Opposite sides of a parallelogram

\[AB = CD,\ BC = DA\]

Common mistake: Asking for extra data the properties already give, such as the other two sides of a parallelogram.

Diagonals of rhombus and kite

Rhombus diagonals bisect each other at right angles. Kite diagonals are perpendicular, and one bisects the other.
For a rhombus side, use Pythagoras on the right triangle formed by the two half-diagonals.

Side of a rhombus

\[s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}\]

Area of a rhombus or kite

\[A = \frac{1}{2} d_1 d_2\]

Common mistake: Using full diagonals in Pythagoras instead of half-diagonals, or forgetting the ½ in the area formula.

Exam tips

Count the given measurements first. A general quadrilateral needs five suitable ones.
Add any given angles to check they can total 360° before constructing.
Draw a rough sketch and label the given parts before using compass and ruler.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

Which of the following is NOT sufficient information to construct a quadrilateral?
Show answer
Answer: B. Three sides and two diagonals
While you can construct a triangle with three sides, a quadrilateral needs more information than just three sides. Two diagonals provide extra information than necessary, leading to ambiguity.
You are given three angles of a quadrilateral as 70°, 80°, and 100°. What is the measure of the fourth angle?
Show answer
Answer: B. 110°
The sum of angles in a quadrilateral is 360°. Therefore, 360° - (70° + 80° + 100°) = 110°
Construct a kite with diagonals of length 10cm and 6cm. What is the area of the kite?
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Answer: A. 30cm²
Area of a kite is half the product of the diagonals (1/2 * 10cm * 6cm = 30cm²).
What's the minimum information required to uniquely construct a cyclic quadrilateral?
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Answer: A. Four sides
Given four sides of a cyclic quadrilateral, you can use Ptolemy's Theorem to find the lengths of the diagonals and then construct the quadrilateral.
Under what conditions is it impossible to construct a quadrilateral given the lengths of its four sides?
Show answer
Answer: B. When the sum of lengths of any three sides is less than the fourth side
This violates the triangle inequality theorem, making construction impossible.