Construction of a triangle given its base and base angle and sum of other two sides
Construction of a triangle given its base and base angle and sum of other two sides
In order to construct a triangle, when its base, sum of the other two sides and one of the base angles are given, we follow the following steps:
Steps of Construction: Obtain the base, base angle and the sum of other two sides. Let BC be the base, be the base angle and x be the sum of the lengths of other two sides AB and AC of
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STEP I Draw the base BC. STEP II Draw STEP III From ray through B making the specified angle, cut-off line segment AX equal to x (the sum of other two sides). |
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STEP IV Join XC. |
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| STEP V: From point C taking radius more than half of CX Draw arc on both side of CX. |  |
| STEP VI : From point X taking same radius as in step V Draw arc on both side of CX to intersect the arcs drawn in step V at point P and Q. |  |
| STEP VII : Join PQ . This is the perpendicular bisector of CX meeting BX at A. |  |
| STEP VIII Join AC to obtain the required triangle ABC. |  |
Justification: Let us now see how do we get the required triangle.
Since point A lies on the perpendicular bisector of CX.Therefore, AX = AC
Now, BA = BX - AX
BA = BX - AC [
AX = AC ]
BX = BA + AC
PROOF
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