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Construction: 1 Mark
Diameter: 1 Mark
The circle can be drawn using a ruler and compass.

The diameter of the circle
$=2\times$ radius $=2\times 10=20cm$

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Each step: 1 Mark
Step 1: Draw a line of length 6 cm. Mark a point P on it.

Step 2: With P as the centre and a convenient radius, construct an arc intersecting the line l at two points A and B.

Step 3: With A and B as centres and a radius 3 cm, construct two arcs, which cut each other at Q.
Step 4: Join PQ. Then PQ is perpendicular to l

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Each steps: 1 Mark
Step 1: Draw a line l. Mark a point Aon theline.

Step 2: Place the compasspointer on the zero mark of the ruler. Open it to place the pencil point up to the 5.6 cm mark.
Step 3: Taking caution that the opening of the compasshas not changed the measured length, place the pointer on A and swing an arc to cut lat B.
Step 4: AB is a line segment of the required length.
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Steps: 2 Marks
Construction: 2 Marks
i) Draw a line segment XY of length 8.4 cm.
ii) Draw a circle, while taking point X as centre and radius more than half of XY.
iii) With same radius and taking thecentre as Y, again draw arcs to cut the circle at A and B. Join AB whichintersects XY at M.
iv) Taking X and Y as centres. Draw two circles more than half of XM.
v)With same radius and taking M as thecentre, draw arcs to intersect these circles at P,Q, R and S.
vi) Join PQ and RS. These are intersecting XY at T and U.
vii) Now XT = TM = MU = UY. These are 4 equal parts of XY.

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Each step: 1Mark
(i) Draw a line segment AB of length 6.8 cm.

(ii) Taking A as the centre, draw a circle by using a compass. The radius of the circle should be more than half of AB.

(iii) With the same radius as before, draw two arcs using B as the centre such that it cuts the previous circle at C and D.

(iv) Join CD. CD is the axis of symmetry.

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Construction: 1 Mark
Solution: 1 Mark
The figure shows aline segment AB.

From a single point, an infinite number of lines can be drawn.
$\therefore$ From point A, infinite lines can be drawn.

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Each step: 1Mark
The steps given below should be followed to construct an angle and its bisector:
i)Draw a line l and mark a point 'O' on it.
ii) Mark a point A ${132}^{\circ }$ to line l with the help of protractor. Join OA.
iii) Draw an arc of convenient radius, while taking point O as the centre. Let it intersect both rays of angle ${132}^{\circ }$ at point A and B.
iv) Taking A and B as centres, draw arcs each of radius more than half of ABso that they intersect each other at C. Join OC.
OC is the required bisector of angle of ${132}^{\circ }$

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Construction of circle: 1 Mark
Construction of chords: 1 Mark
Construction of bisector: 1 Mark
Meeting point: 1 Mark
i)Mark any point C on the sheet. Now, by adjusting the compassup to 3 cm and by putting the pointer of compass,draw the circle. It is the required circle of 3 cm radius.
ii)Take any two chords AB and CD in the circle.
iii)Taking A and B as centres and with radius more than half of AB, draw arcs on both sides of AB, intersecting each other at E, F. Join EF which is the perpendicular bisector of AB.
iv)Taking C and D as centres and with radius more than half of CD, draw arcs on both sides of CD, intersecting each other at G andH . Join GH which is the perpendicular bisector of CD.
Now, we find thatEF and GH meet at the centre of circle O.

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(a)2Marks
(b)2Marks
(a) The steps given below should be followed to construct an angle and its bisector:
i)Draw a line l and mark a point 'O' on it.
ii)Mark a point A at ${115}^{\circ }$ with the help of protractor. Join OA.
iii)Draw an arc of convenient radius, while taking point O as the centre. Let it intersect both rays of the ${115}^{\circ }$ angle at point A and B.
iv)Taking A and B as centres, draw an arc of radius more than $\frac{1}{2}$ AB in the interior of the angle of ${115}^{\circ }$. Let those intersect each other at C. Join OC.
OC is the required bisector of the angle of ${115}^{\circ }$.

(b)As usual, we will have to use only a straight edge and the compass.
Given $\angle A$, whose measure is not known.

Step 1: Draw a line l and choose a point P on it.

Step 2: Place the compassat A and draw an arc to cut the rays of $\angle A$ at B and C.

Step 3: Use the same compasssetting to drawan arc with P as centre, cutting l in Q

Step 4: Set your compassto the length BC with the same radius.

Step 5: Place the compasspointer at Q and draw the arc to cut the arc drawn earlier in R.

Step 6: Join PR. This gives us $\angle P$. It has the same measure as $\angle A$.

This means $\angle QPR$ has the same measure as $\angle BAC$.

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Definition: 1 Mark
Construction: 1 Mark
Aline segmentis a part of alinethat is bounded by two distinct end points, and contains every point on thelinebetween its endpoints.