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Construction of a Square When a Diagonal Is Given.

To construct ...

Question

To construct the perpendicular bisector of a line segment AB, first we have to draw the line segment AB. Then, with A as centre, at what radius should be set the compass for drawing the arcs ?

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Solution

The Compass should be set at a radius of more than $\frac{1}{2}$ of AB

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Q. To construct perpendicular bisector to a line segment AB =10 cm, we have to draw an arc of radius

Write correct sequence of the following steps to draw perpendicular bisector of a line AB.

a. Join XY to cut AB at O. XY is called the perpendicular bisector of AB.

b. To construct the perpendicular bisector of the line segment AB, we first take A and

then B as centre and radius greater than half of AB.

c. Draw arcs above and below AB such that the arcs cut each other at X and Y.

Q. Steps for the construction of perpendicular bisector PQ to a line segment AB of given length is given below. Choose the correct order.
1.With B as the centre and the same radius as in previous step, draw two arcs to intersect the arcs drawn in previous step. Name the point of intersection of the arcs as P and Q
2.Draw a line segment AB of given length using a scale.
3.Join P and Q.
4.With A as the centre and radius more than half of AB, draw two arcs (using compases) above & below AB

Q. Draw a line segment AB = 5.6 cm. Draw the perpendicular bisector of AB.

Q. To construct a trapezium ABCD with

A B ∥ C D,

AB = 8 cm, BC = 5 cm, AD = 6 cm and

∠ A B C = 60^{\circ},

we follow the following steps:
1) Draw the line segment AB = 8 cm.
2) Construct the angle

∠ A B X = 60^{\circ}

at B.
3) With B as centre, draw an arc of radius 5 cm cutting BX at C.

The next step is ___.

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Construction of a Square When a Diagonal Is Given.

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