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Question

# A student was given the following details while constructing a triangle ABC: The length of the base of the triangle BC, one of the base angles say ∠ B and the sum of the other two sides of the triangle (AB+AC) He went about the construction of this triangle by first drawing the base of the triangle BC. He then drew an angle at the point B equal to the given angle on a ray that he drew. After completing these steps, he got stuck and doesn’t know what to do next. Which of the following steps will he take up next?

A

Cut a line segment BD equal to (AB+AC) on that same ray

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B

Change the base length to (AB+AC) and then draw one of the base angles at one of the ends of the line segment whose length is equal to (AB+AC)

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C

He knows the perimeter of the triangle, he changes the base length to that of the perimeter of the triangle and then draws one of the base angles at one of the ends of the line segment

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D

Cut a line segment BD equal to 2(AB+AC) on that same ray

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Solution

## The correct option is A Cut a line segment BD equal to (AB+AC) on that same ray We have been given the base length and a base angle, which means half the job is already done for us. We need to draw the base with the given length and draw a ray with an angle = base angle, after that we must cut a line segment BD equal to (AB + AC) on that same ray so as to perpendicularly bisect the ray DC and have AD = AC because A is the point where the perpendicular bisector of ray DC cuts BD.

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