Practical Geome...

Given below are the steps for construction of a quadrilateral ABCD, where AC = 5.5 cm, BD = 7 cm, BC = 4.5 cm, AD = 5.5 cm and CD = 5 cm. Which of the following steps is incorrect?

Step (1): Draw AC = 5.5 cm.
Step (2): With A as the centre and radius 5.5 cm, draw an arc.
Step (3): With C as the centre and radius 5 cm draw another arc, cutting the previous arc at D. Join AD and DC.
Step (4): With D as the centre, draw an arc of radius 7 cm on the opposite side of AC.
Step (5): With C as the centre, draw an arc of 5 cm cutting the arc drawn in above step at B.
Step (6): Join AB, BC and BD.

Draw a parallelogram MATH, where MA = 5.6 cm and AT = 4.8 cm. Is the given information sufficient for that?

Arrange the steps for the construction of a quadrilateral ACBD, where AB = 4.5 cm, BC = 5 cm, CA = 6 cm, DA = 5.5 cm and DB = 7.5 cm.

(1) Join DA and DB.
(2) Draw an arc of radius 5.5 cm taking A as the centre. Then, draw another arc of radius 7.5 cm taking B as the centre. Both arcs intersect at D.
(3) Draw AB = 4.5 cm.
(4) Join CA and BC.
(5) Draw arcs of radii 6 cm and 5 cm taking A and B, respectively, as centres, at opposite sides which intersect at C.

Arrange the steps for construction of a parallelogram ABCD, where AB = 6 cm, BC = 7 cm and angle B = 85.

(1) Join AD and CD.
(2) Cut an arc of radius 7 cm from point B and let this point be C.
(3) Draw an arc of radius 7 cm taking A as the centre. Draw another arc of radius 6 cm taking C as the centre.
(4) Draw an angle at B = 85°.
(5) Draw a line segment AB = 6 cm.

Which of the following quadrilaterals can be formed using the information given below:

Diagonals AC = 5.4 cm and BD = 6.2 cm bisect each other and one of the angles between them is 70°.

Given below are the steps for construction of a quadrilateral ABCD, where AB = 4.6 cm, ∠ABC = 80°, BC = 5 cm, ∠BAD = 120° and AD = 6 cm. Which of the following steps is/are INCORRECT?

Step 1: Draw AB = 4.6 cm.
Step 2: Make ∠ABX = 80°.
Step 3: With B as the centre and radius equal to 6 cm, draw an arc cutting BX at C.
Step 4: Make ∠BAY = 120°.
Step 5: With A as the centre and 5 cm as radius, draw an arc cutting AY at D.
Step 6: Join CD.

To construct a trapezium, which of the following pieces of information is sufficient?

Which of the following statements is/are true for the construction of a kite ABCD, where AB = 5 cm, BC = 6 cm, CD = 5 cm and BD = 7 cm?

(A) It is possible to draw the kite.
(B) It is not possible to draw the kite because AB = CD.
(C) It is not possible as BC ≠ AD.
(D) It is not possible to draw the kite because AB ≠ BC and AD ≠ CD.

To construct a quadrilateral JUMP, which of the following pieces of information is necessary?

What information about a square is necessary in order to construct it?

Arrange the steps for construction of a rectangle ABCD, where AB = 7 cm and BC = 8 cm.

(1) Draw angle ZAB = 90° and angle YBA = 90°.
(2) Draw an arc of radius 8 cm taking A as the centre and mark it as D. Draw another arc of radius 8 cm taking B as the centre and mark it as C.
(3) Join C and D.
(4) Draw a line segment AB = 7 cm.

Match the following:

Arrange steps (a) to (d) in correct order in relation to the construction of a parallelogram LMNO, where LM = 8 cm, MN = 5 cm and diagonal LN = 6 cm.

First, draw LM = 8 cm.

(a) With L as the centre, draw an arc of radius 6 cm to cut the arc drawn in previous step.
(b) Join NO and LO.
(c) With N and L as centres, draw arcs of radii 8 cm and 5 cm, respectively, which cut each other at O.
(d) With M as the centre, draw an arc of radius 5 cm.

In which of the following cases can a convex quadrilateral be constructed?

(a) If two diagonals and three sides are given
(b) If three sides and one included angle are given
(c) If four sides and one diagonal are given
(d) If two adjacent sides and two angles are given

Given below are the steps required for the construction of a rhombus when the lengths of two diagonals are given. Which of the following steps is/are incorrect in construction of a rhombus LMNO, where LN = 8 cm and MO = 6 cm?

Step 1: Draw a line segment LN of length 8 cm.
Step 2: Draw a perpendicular bisector of side LN by drawing arcs from L and N both above and below the side.
Step 3: Cut arcs of radius 3 cm from the point of intersection of perpendicular bisector and LN on either side of LN. Let these points be M and O.
Step 4: Join L and M, M and N, L and O, N and O, and M and O.
Step 5: LMNO is the required rhombus.