Question

Q31. Construct a triangle CA=6cm, AB= 5cm BAC=45° and then construct triangle whose sides are 3/5 of the
corresponding sides of triangle ABC.
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Answer 1

Steps of Construction :

1.    Draw a line segment AB = 5 cm.

2.    At A make ∠BAY = 45°.

3.    Take A as centre and radius = AC = 6 cm (= CA), draw an arc cutting AY at C.

4.    Join BC to obtain the triangle ABC.

5.    Draw any ray AX making an acute angle with AB on the side opposite to the vertex

C.

6.    Mark off 6 points (the greater of 6 and 5 in 6/5) A1, A1, A3, A4,A5 and A6 on AX so

that

AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6

7.    Join A5 (the 5th point, being the smaller of 5 and 6 in 5/6) to B and draw a line through A6 parallel to A5B intersecting the extended line segment AB at B’.

8.    Draw a line through B‘C’ parallel to BC intersecting the extended line segment AC at C’.