CBSE Class 8 Maths The Baudhayana-Pythagoras Theorem (Class 8 NCERT New) Quiz 2

1. Is less than or greater than ?

A Less than B Equal to C Greater than

2. Will we ever get a number with a terminating decimal representation whose square is ?

A Yes, a terminating decimal can square to B No, a terminating decimal cannot square to

3. Can be expressed as a fraction , where and are counting numbers?

A Yes, equals a fraction of counting numbers B No, cannot be expressed as a fraction of counting numbers

4. Two identical square papers are cut as shown into triangular pieces labeled 1–4. Can these pieces be arranged to create a square with double the area of either square?

A Yes, the pieces can be arranged into such a square B No, the pieces cannot form such a square

5. The length of the two equal sides of an isosceles right triangle is . Choose bounds on the hypotenuse that have at least one digit after the decimal point.

A Between and B Between and C Between and D Between and

6. What construction allows two squares of different sizes to be combined to make a larger square whose area equals the sum of the areas of the two smaller squares?

A Make a right-angled triangle whose perpendicular sides are the sidelengths of the two squares and take the square on its hypotenuse B Place the smaller square entirely inside the larger and connect opposite corners C Rotate one square by and overlay it on the other D Join the squares edge-to-edge to form a rectangle and square the rectangle’s area

7. Why does Baudhāyana’s method work?

A Because in a right triangle, the area of the square on the hypotenuse equals the sum of the areas of the squares on the two perpendicular sides B Because any two squares can be rearranged to have equal areas by cutting and pasting C Because the perimeter of the larger square equals the sum of the perimeters of the smaller squares D Because the hypotenuse is always equal to the sum of the other two sides

8. When the two original squares are the same size, does Baudhāyana’s method agree with the earlier method used to combine two identical squares into a bigger square?

A Yes, it agrees; the square on the diagonal of a right triangle with equal legs matches the earlier construction B No, it does not agree; the resulting square has a different area C It agrees only when each square has area D It cannot be determined without measurement

9. In the construction where four congruent right triangles labeled T, U, W, and X are arranged around a central quadrilateral V to form a 4‑sided figure over the hypotenuse, which statement best explains why all four sides of the new 4‑sided figure are equal in length?

A Because T, U, W, and X are congruent, the segments they touch along the boundary are equal, making all sides equal B Because V is a square, each outer side automatically equals its diagonal C Because the areas of T, U, W, and X are different, their side lengths must compensate to be equal D Because the hypotenuse of each triangle is parallel to the base of the large square

10. In the same 4‑piece arrangement, angle labels near the corners show x and 90 − x at adjacent angles around the boundary. What justifies that each corner angle of the new 4‑sided figure is a right angle, so the figure is a square?

A Each corner combines angles x and 90 − x to total , giving four right angles B Each corner is an exterior angle of triangle V, so it must be C Opposite sides are parallel, so each interior angle is D Congruence of T, U, W, and X forces all interior angles to be equal but not necessarily right angles