Quadrilaterals — Quiz

Q1. Ravi draws a figure with four straight line segments, but the last segment does not meet the first. Why is his figure NOT a quadrilateral?

• A. Because all the angles are not equal
• B. Because it has fewer than four sides
• C. Because the sides are of different lengths
• D. Because the figure is not closed

Q2. In a quadrilateral, the angles are located

• A. Only at one corner
• B. In the middle of each side
• C. On the diagonals
• D. At the points where two sides meet

Q3. In the Carpenter's Problem two wooden strips are placed and then a thread is run through their endpoints. The figure formed by the thread is a rectangle when the strips

• A. Are of equal lengths and joined at their midpoints
• B. Are of unequal lengths and meet at one end
• C. Are perpendicular but unequal
• D. Touch each other only at their tips

Q4. Priya wants to construct a square using two wooden strips and a thread. Beyond the rectangle conditions, what extra step does require?

• A. Make the strips touch only at their ends
• B. Use four strips instead of two
• C. Make the strips bend slightly
• D. Make the diagonals meet at an angle of 90°

Q5. In square ABCD, the diagonal AC is drawn. By Property 5 what is the measure of ∠1 (the angle that AC makes with side AD at vertex A)?

• A. 45°
• B. 30°
• C. 60°
• D. 90°

Q6. Asks whether a quadrilateral can have three angles equal to 90° and the fourth NOT equal to 90°. Which of these explains why this is impossible?

• A. Because a quadrilateral has only three angles in total
• B. Because the fourth angle is always 180°
• C. Because right angles only occur in pairs
• D. Because the four angles must add up to 360°, so 90° + 90° + 90° forces the fourth to be 90°

Q7. The angle sum of a quadrilateral SOME is proved by drawing diagonal SM. The proof rests on which key fact?

• A. The two triangles formed each have an angle sum of 180°
• B. Both diagonals of a quadrilateral are equal
• C. The diagonal divides the quadrilateral into two equal areas
• D. Each diagonal is parallel to one side

Q8. Anita finds a quadrilateral in which all four angles are equal. Using the angle-sum result each angle measures

• A. 90°
• B. 60°
• C. 45°
• D. 120°

Q9. On, in parallelogram ABCD with ∠A = 30°, deduces ∠D = 150°. The reason given is that AB ∥ CD and

• A. AD is a transversal, so co-interior angles on the same side add to 180°
• B. Opposite angles of a parallelogram are supplementary
• C. All angles of a parallelogram are equal
• D. AD is parallel to BC, so ∠A = ∠D

Q10. In a parallelogram PQRS, ∠P = 75°. Using the parallelogram-angle property , ∠Q equals

• A. 75°
• B. 150°
• C. 115°
• D. 105°

Q11. On, Property 4 of a parallelogram states that its diagonals

• A. Bisect each other
• B. Are always equal in length
• C. Are perpendicular to each other
• D. Bisect the interior angles

Q12. (Deduction 10) shows that in rhombus GAME, the diagonals intersect at

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Q13. The constructed rhombus ABCD has ∠A = 50°. It follows that ∠B equals

• A. 130°
• B. 65°
• C. 50°
• D. 150°

Q14. A kite ABCD is defined as a quadrilateral in which

• A. All four sides are equal
• B. The diagonals are equal and bisect each other
• C. AB = CD and BC = DA (opposite sides equal)
• D. AB = BC and CD = DA (two pairs of adjacent sides equal)

Q15. A Class 8 teacher draws the Venn diagram from. She points to the smallest yellow region labelled 'square' inside both 'rectangle' and 'parallelogram'. This is meant to show that every square is

• A. Both a rectangle AND a parallelogram
• B. A different figure from a rectangle
• C. Neither a rectangle nor a parallelogram
• D. Only a parallelogram, not a rectangle