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Construct with ruler and compasses, angles of following measures: (a) 60⁰ (b) 30⁰ (c) 90⁰ (d) 120⁰ (e) 45⁰ (f) 135⁰

Solution: (a) 600 To construct an angle of 600 the following steps can be followed (i) Draw a line l and mark a point P on it. Consider P... View Article

Draw an angle of measure 153⁰ and divide it into four equal parts.

Solution: To construct an angle of measure 1530 and its bisector listed below are the steps that are to be followed (i) Draw a line l and... View Article

Draw a right angle and construct its bisector.

Solution: To construct a right angle and its bisector listed below are the steps that are to be followed (i) Draw a line l and mark a point P... View Article

Draw an angle of measure 147⁰ and construct its bisector.

Solution: To construct an angle of measure 1470 and its bisector listed below are the steps that are to be followed (i) Draw a line l and mark... View Article

Draw ∠POQ of measure 75⁰ and find its line of symmetry.

Solution: To construct an angle of 750 and its line of symmetry listed below are the steps that are to be followed (i) Draw a line l and... View Article

Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of [latex]overline{OA}[/latex] and [latex]overline{OB}[/latex] Let them meet at P. Is PA = PB?

Solution: (1) Draw any angle with vertex as O. (2) By considering O as centre and with convenient radius, draw arcs on both rays of... View Article

Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

Solution: (1) Locate any point O on the sheet. Now adjust the compasses up to 4 cm and by setting the pointer of compasses at point O, turn the... View Article

Draw a circle with centre C and radius 3.4 cm. Draw any chord[latex]overline{AB}[/latex]. Construct the perpendicular bisector of [latex]overline{AB}[/latex] and examine if it passes through C.

Solution: (1)Locateany point C on the sheet (2) Adjust the compasses up to 3.4 cm and by putting the pointer of compasses at point C, turn... View Article

With [latex]overline{PQ}[/latex] of length 6.1 cm as diameter, draw a circle.

Solution: (1) Draw a line segment of 6.1 cm (2) Consider point P as centre and radius more than half of , draw a circle (3)... View Article

Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.

Solution: (1)Draw a line segment of 12.8 cm (2) By considering point X as centre and radius more than half of XY, draw a circle. (3)... View Article

Draw the perpendicular bisector of [latex]overline{XY}[/latex] whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY. (b) If M is the mid point of [latex]overline{XY}[/latex], what can you say about the lengths MX and XY?

Solution: (1) Draw a line segment of 10.3 cm (2) Consider point X as centre and draw a circle by using compasses. The radius... View Article

Draw a line segment of length 9.5 cm and construct its perpendicular bisector.

Solution: To construct a line segment of length 9.5 cm and to construct its perpendicular bisector the steps given below can be followed (1)... View Article

Draw [latex]overline{AB}[/latex] of length 7.3 cm and find its axis of symmetry.

Solution: To construct of length 7.3 cm and find its axis of symmetry the steps given below can be followed (1) Draw a line... View Article

Draw a line l and a point X on it. Through X, draw a line segment [latex]overline{XY}[/latex] perpendicular to l.Now draw a perpendicular to XY at Y. (use ruler and compasses)

Solution: (1)Draw a line l and mark a point X on it. (2) By considering X as centre and with a convenient radius, draw an arc intersecting... View Article

Draw any line segment [latex]overline{PQ}[/latex] Take any point R not on it. Through R, draw a perpendicular to [latex]overline{PQ}[/latex] (use ruler and set-square)

Solution: (1) Draw a given line segment (2) Place a set square on (3) Now, place the ruler along the edge opposite to... View Article

Draw any line segment [latex]overline{AB}[/latex] Mark any point M on it. Through M, draw a perpendicular to [latex]overline{AB}[/latex](use ruler and compasses)

Solution: (1) Draw a line segment and mark a point M on it. (2) Considering M as centre and a convenient radius, construct an arc... View Article

Given some line segment [latex]overline{AB}[/latex], whose length you do not know, construct [latex]overline{PQ}[/latex] such that the length of [latex]overline{PQ}[/latex] is twice that of [latex]overline{AB}[/latex].

Solution: To construct a line segment (1) Let the given line segment be (2) Adjust the compasses up to the length of ... View Article

Draw any line segment PQ Without measuring PQ construct a copy of PQ

Solution: (1) Let the given line segment be (2) Adjust the compasses up to the length of (3) Draw any line l and mark a point A on it... View Article

Given [latex]overline{AB}[/latex] of length 7.3 cm and [latex]overline{CD}[/latex] of length 3.4 cm, construct a line segment [latex]overline{XY}[/latex] such that the length of [latex]overline{XY}[/latex] is equal to the difference between the lengths of [latex]overline{AB}[/latex] and [latex]overline{CD}[/latex]. Verify by measurement.

Solution: (1) Given that = 3.4 cm (2) Adjust the compasses up to the length of CD and place the pointer of compasses at point A, draw... View Article

Given [latex]overline{AB}[/latex] of length 3.9 cm, construct [latex]overline{PQ}[/latex] such that the length of [latex]overline{PQ}[/latex] is twice that of [latex]overline{AB}[/latex]. Verify by measurement.

Solution: We can draw a line segment by following the steps given below (1) Draw a line l and mark a point P on it. Let AB be the... View Article

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