Construction of a triangle given its perimeter and its two base angles
Construction of a triangle given its perimeter and its two base angles
Construction of Triangle Given Its Perimeter and Its Two Base Angles: In order to construct a triangle of given perimeter and two base angles, we follow the following steps:
Steps of Construction: Obtain the perimeter and the base angles of the triangle.Let ABC be a triangle of perimeter p cm and base BC.
STEP I Draw a line segment XY equal to the perimeter p of STEP II Construct |  |
| STEP III : Draw bisectors of angles |  |
| STEP IV: Draw the perpendicular bisectors PQ, RS of XA and YA meeting XY in B and C respectively. |  |
| STEP V Join AB and AC to obtain the required triangle ABC. |  |
Justification: For the justification of the construction, we observe that B lies on the perpendicular bisector of AX.
XB = AB
[ Angles opposite to equal sides are equal]
Similarly, C lies on the perpendicular bisector of AY.
YC = AC
Now, XY = XB + BC + CY
XY = AB + BC + AC
In we
[Exterior angle is equal to the sum of interior opposite angle]
[because the angles are equal Proved above]
[ AX is the bisector ]
= [By Step II of Construction]
In we have
[Exterior angle is equal to the sum of interior opposite angle]
[because the angles are equal Proved above]
[ AY is the bisector ]
[By Step II of Construction]
Example: Construct a triangle PQR whose perimeter is equal to 14 cm, and
.
SOLUTION To draw we follow the following steps:
Steps of Construction:
STEP I Draw a line segment XY = 14 cm STEP II Construct |  |
| STEP III Draw the bisectors of angles |  |
| STEP IV Draw right bisector AB, CD of RX and RY meeting XY at P and Q respectively. |  |
| STEP V Join PR and QR to obtain the required triangle PQR. |  |
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