Question

Construct a triangle ABC in which BC = 8cm, $\angle B={{45}^{\circ }}$ and AB – AC = 3.5cm.

Answer 1

Hint: To draw this construction we will first draw BC of length 8cm. Now draw BZ such that $\angle B={{45}^{\circ }}$. Now measure the arc of length AB – AC = 3.5cm. With this measure draw an arc from point B such that it intersects BZ at D. Then join CD and draw a perpendicular bisector for CD. Let this perpendicular bisector cut BZ at A. Now join AC, hence we get triangle ABC

Complete step-by-step solution
Now first let us construct triangle ABC.
Now we have a length of BC = 8cm
Hence let us first draw line segment BC of length 8cm.
To do this first draw a line and mark point B.
Now from point B draw an arc of radius 8cm. Now the point where it cuts the line segment is our point C.

Now with the help of a protractor, draw a line segment BZ such that the angle of this line with BC is 45 degrees.

Now we have AB – AC = 3.5cm.
Now from point B draw an arc with a radius of 3.5cm.
Let this arc cut line BZ on point D.

Now we want to draw a perpendicular bisector for CD.
Now let us see the steps to draw the perpendicular bisector
Now from point D draw two arcs of any radius such that one arc is above CD and one arc is below CD.
Now with the same radius again draw two arcs from point C such that one arc is above CD and one arc is below CD.
Hence we will get a figure like this.

Now we have two intersection points of arcs. We will join them by a line Now extend the line to intersect BZ let this intersection point be called A.

Now join AC and hence we will get our required triangle ABC.

Note: Now while drawing a side of length say 8 cm we can directly draw it with scale but for precise measurements, we use the arc method, Also to precisely measure 45 degrees use the perpendicular bisector method of construction.
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