Class 6 Maths, Chapter 8 (NCERT). 15 questions by concept, 15 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
Use the figure. AB is the straight endpoint-to-endpoint line of a semicircle, and X is its centre. What compass opening AX is needed?
(c) 6 cm
AB is the diameter of the semicircle. The centre X is halfway between A and B, so the compass opening AX is half of AB: 12 / 2 = 6 cm.
The figure shows a wave pattern outline with one curved part marked ?. The centre O of that curve is also shown. Choose the correct rule for drawing this semicircle with a compass.
(a) A compass can draw only the needed semicircle of the circle.
A compass can draw only the needed semicircle of a circle. It does not have to draw a complete circle before the wave pattern curve is made.
Use the figure. AX is the compass radius for one semicircle in a wave pattern. What is the straight endpoint-to-endpoint length AB for that semicircle?
(a) 6 cm
AX is the radius. The straight endpoint-to-endpoint length AB is the diameter, which is twice the radius: 2 * 3 = 6 cm.
Complete the name of the rectangle by starting at A and travelling clockwise around the boundary. Which completed name is correct?
(b) ABCD
The corners in order around the boundary are A, B, C, D clockwise, and A, D, C, B anticlockwise. Follow neighbouring corners in the same direction all the way around. Starting at A and travelling clockwise gives ABCD.
The rectangle has corners A, B, C, D in order around the boundary. The proposed name is DBAC. Where is the first jump across the rectangle?
(a) D to B
The first move is from D to B. These are opposite corners, so this move crosses the shape.
In the figure, several straight lines pass through point Q on line m. How many of these lines are truly perpendicular to m?
(c) One
Only the candidate making a right angle with m is perpendicular. The slanting candidates merely intersect it.
In the figure, line l is horizontal and point P lies on it. Three rays start from P. Which ray is perpendicular to line l?
(d) Ray A, the ray making a angle with line l
The ray perpendicular to a horizontal line must make a angle with it. In the figure, ray A is the vertical ray, so ray A is perpendicular to line l.
Use the figure to start constructing rectangle ABCD. The breadth is 2 cm. Which construction rule correctly completes the rectangle?
(c) AB = CD = 7 cm; AD = BC = 2 cm; four right angles
A rectangle needs four right angles and equal opposite sides. Here AB = CD = 7 cm and BC = AD = 2 cm.
In the figure, A, B and D are already placed for rectangle ABCD. Where is the missing vertex C?
(c) On the perpendicular through B, with BC = 5 cm and CD = 6 cm
C lies on the perpendicular through B with BC = AD = 5 cm. Then CD = AB = 6 cm.
In the figure, PQRS is a rectangle and diagonal PR is drawn. What conclusion must follow about the adjacent sides PQ and PS?
(d) PQ = PS, so PQRS is a square.
The diagonal divides the right angle at P into 45° and 45°. Equal splitting of a right angle by the diagonal happens in this rectangle only when the adjacent sides are equal, so the rectangle is a square.
Use the figure of rectangle PQRS. The diagonal PR was measured with a ruler and found to be 7.2 cm. The other diagonal QS is marked ?. What length should be recorded for QS?
(c) 7.2 cm
A side is part of the boundary, while a diagonal joins two opposite vertices. QS joins the opposite vertices Q and S, so QS is a diagonal and not a side. Measuring the two diagonals of a rectangle with a ruler gives the same length for both. PR measures 7.2 cm, so QS measures 7.2 cm as well.
Rectangle ABCD has AB = 6 cm and AD = 12 cm. X lies on side AD and Y lies on side BC. The table gives four possible pairs of positions. Which row makes ABYX a rectangle?
| Row | AX (cm) | BY (cm) |
|---|---|---|
| A | 6 | 6 |
| B | 8 | 6 |
| C | 8 | 9 |
| D | 9 | 8 |
(a) Row A: AX = 6 cm, BY = 6 cm
ABYX is a rectangle when X and Y are the same distance from A and B: AX = BY. Only Row A has both distances equal to 6 cm. All the listed distances are shorter than the 12 cm sides, so X and Y lie on those sides.
In rectangle ABCD, X is on AD and Y is on BC. AB = 13 cm and AD = 11 cm. AX = BY = 6 cm, so ABYX has four right angles. What is the length of XY?
(c) XY = 13 cm
ABYX is a rectangle, so its opposite sides XY and AB are equal. Therefore XY = 13 cm.
In the figure, B and C must lie on one arc marked ?. What centre and radius draw that arc?
(b) Centre A, radius 4 cm
AB and AC are both 4 cm. An arc centred at A with that radius passes through B and C.
Two arcs of radius 4 cm are centred at B and C. Which marked point is 4 cm from both centres and lies below BC?
(a) Q, below BC
The required point lies on both arcs and on the below side of BC. That point is Q.
Wrong
Four equal sides always make a square.
Why it feels right. Equal sides are the first feature I remember about squares.
Right
A square also has four right angles.
Worked example
