Question

Construct a \[\Delta ABC\] in which \[BC = 8cm\], \[\angle B = 45^\circ \] and \[AB - AC = 3.5cm\] .

Answer 1

Hint:
Here, we have to construct a triangle ABC. A triangle has to be constructed with the given conditions. A triangle is a two-dimensional shape with three edges and three vertices. It is one of the basic shapes in Geometry. The sum of the three interior angles of a triangle is always \[180^\circ \].

Complete step by step solution:
We will use the following steps to construct a \[\Delta ABC\] with\[BC = 8cm\], \[\angle B = 45^\circ \] and \[AB - AC = 3.5cm\].
1) We will draw a line segment \[BC = 8cm\] .

                             B \[8cm\] C
2) We will then construct an angle \[\angle B = 45^\circ \] at Point \[B\].

3) Now, we have to cut the line segment \[BX\] at \[D\] from \[B\] with \[BD = 3.5cm\] i.e., \[AB - AC = 3.5cm\].
4) Now we will join \[CD\]

5) Now, we will draw a perpendicular bisector of \[CD\].

6) The perpendicular bisector \[PQ\] intersects the ray \[BX\] at point \[A\].
7) Now we will join \[CA\] .

8) The triangle \[\Delta ABC\] thus formed is the required triangle.

Note:
A perpendicular bisector can be defined as a line segment which intersects another line perpendicularly and divides it into two equal parts. Two lines are said to be perpendicular to each other when they intersect in such a way that they form \[90\] degrees with each other. And, a bisector divides a line into two equal halves. Thus, a perpendicular bisector of a line segment \[AB\] implies that it intersects \[AB\] at \[90\] degrees and cuts it into two equal halves. Every point in the perpendicular bisector is equidistant from point A and B. Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints.