Which of the following figures show the correct method to construct a triangle if we know its base, a base angle and sum of other two sides?

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Solution

The correct option is A

The correct procedure to construct the given triangle is:
1. Draw the base BC of $Δ$ ABC as given and construct $∠$ XBC of the required measure at B as shown.

2. Keeping the compass at point B cut an arc from the ray BX such that its length equals to AB + AC at point P and join it to C as shown.

3. Now measure $∠$ BPC and from C draw an angle equal to $∠$ BPC as shown.

Thus, option A is correct.

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