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प्रश्न
Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct a ΔABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60°.
(ii) Construct the locus of the vertices of the triangles with BC as base, which are equal in area to ΔABC.
(iii) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(iv) Measure and record the length of CQ.
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उत्तर
Steps of Constructions:
(i) (1) Mark a horizontal line XY on your paper and take BC = 6 cm on it.
(2) Construct ∠ABC = 60° with arm AB = 9 cm.
(3) Join A and C to get the required ΔABC.
(ii) (1) Draw AD ⊥ BC.
(2) Construct a line X'Y', perpendicular to AD, parallel to XY and passing through A.
(3) X'Y', is the required locus of the vertices of Δs with base BC and area to ΔABC.
[∵ Δs having same base and height an equal in area]
(iii) (1) Draw right bisector PQ of BC, meeting X'Y', in Q.
(2) Then Q is the point such that ΔQBC is an isosceles triangle and area (ΔQBC) = area (ΔABC).
(iv) On measuring, we find CQ = 8·4 cm.
संबंधित प्रश्न
Use ruler and compasses only for this question:
I. Construct ABC, where AB = 3.5 cm, BC = 6 cm and ABC = 60o.
II. Construct the locus of points inside the triangle which are equidistant from BA and BC.
III. Construct the locus of points inside the triangle which are equidistant from B and C.
IV. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and records the length of PB.
On a graph paper, draw the lines x = 3 and y = –5. Now, on the same graph paper, draw the locus of the point which is equidistant from the given lines.
Describe the locus of vertices of all isosceles triangles having a common base.
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Using ruler and compasses construct:
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(iii) a circle touching AB at A and passing through C.
