State True or False.

If we draw a triangle ABC, with side BC=6.5cm, ∠B=30°, ∠A =105°, then construct another triangle whose sides are 3/4 times the corresponding sides of the triangle ABC, the construction looks like the following figure.

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True

False

answer is A.

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Detailed Solution

We know that sum of angles of a triangle is 180⁰.
∠A + ∠B + ∠C = 180⁰
105⁰+ 30⁰ + ∠C = 180⁰
135⁰ + ∠C = 180⁰
∠C = 45⁰
Draw a line segment BC = 6.5 cm.
Draw an angle ∠B = 30⁰ with B as a centre and draw an angle ∠C = 45⁰ with C as a centre.
Extend the lines, so that they intersect at a point A.
Thus, ∆ABC is the given triangle.
Question Image

Now, draw a ray BX that makes acute angle with line segment BC on the opposite side of vertex A.
Mark 4 points, say B1, B2, B3, B4 on the ray BX, such that BB1=BB2=BB3=BB4.
Now join B4 and C.
Draw a line from B3 which is parallel to B4C.
Let it intersect BC at C`.
Now draw a line through C` which is parallel to line AC and let it intersect AB at A`.
So, A’BC` is the required triangle.
Question Image

So, the given figure is true.
The correct option is (1).

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