CBSE Class 8 Maths The Baudhayana-Pythagoras Theorem (Class 8 NCERT New) Quiz 1

1. How can one construct a square having double the area of a given square? Choose the method that always works for any square.

A Double the length of each side of the given square B Construct a square on the diagonal of the given square C Rotate the given square by 45 degrees without changing side length D Join the midpoints of two adjacent sides of the square

2. Why does the new dotted square have double the area of the original square? The figure shows a square with a tilted (dotted) square built on its diagonal.

A Because each side of the dotted square is twice as long as a side of the original square B Because the original square can be partitioned into two equal triangles, while the dotted square can be partitioned into four congruent triangles of the same size C Because the dotted square’s perimeter is twice that of the original square D Because the dotted square and the original square have equal diagonals

3. Why should the extensions of the vertical and horizontal sides of the original square pass through the vertices of the dotted square?

A They are angle bisectors of the dotted square and therefore pass through the opposite vertices B They are parallel to the sides of the dotted square and therefore intersect them at right angles C They are perpendicular bisectors of the original square’s sides and so avoid the dotted square D They lie along the medians of the dotted square and therefore meet at its center only

4. All the small triangles formed by the horizontal and vertical guidelines in the construction are congruent to each other. Which justification best explains this?

A Side–Angle–Side congruence using equal halves of sides and equal included angles B Angle–Side–Angle congruence using two right angles and any side C Hypotenuse–Leg congruence for obtuse triangles D No triangles are congruent because their orientations differ

5. After cutting two identical squares of paper as shown and placing pieces 5, 6, 7, and 8 around Square 1, what figure do you obtain?

A A rectangle with the same area as Square 1 B A square with double the area of Square 1 C A square with half the area of Square 1 D A rhombus with the same area as Square 1

6. We want a square whose area is half that of a given square. Which construction achieves this?

A Draw a tilted square by joining the midpoints of the sides of the original square B Draw a square on the diagonal of the original square C Halve the side length of the original square D Rotate the original square by 90 degrees

7. Why is the smaller inside square half the area of the larger square?

A Its diagonal equals the larger square’s side length B It consists of exactly two of the four congruent triangles formed by drawing the east–west and north–south lines through the large square’s center C Its perimeter is half the perimeter of the larger square D Its side length is half that of the larger square

8. Using paper folding, how can you make a square whose area is half the area of the first square?

A Fold each corner to the center so creases pass through the midpoints of the sides; the diamond PQRS formed is the required square B Fold the paper in half along one side and cut along the fold C Fold along a diagonal and cut off one triangular half D Fold each side outward to extend the square

9. Will a square having half the side length of the original square have half the area?

A Yes; halving side length halves the area B No; halving side length makes the area one-fourth of the original, so four such squares fill the original C Yes; two such smaller squares will fill the original D No; halving side length makes the area one-third of the original

10. Why is PQRS a square, and why is its area half that of the original paper after folding all four corners to the center?

A PQRS has equal sides and right angles formed by perpendicular creases; it is composed of two of the four congruent corner triangles, giving half the area B PQRS is a rectangle with unequal sides; it covers one-third of the paper C PQRS is a rhombus without right angles; it covers three-fourths of the paper D PQRS is any quadrilateral; its area equals the whole paper