# Triangle Construction: Given its Perimeter and Two Angles

Given: The Perimeter of the triangle and two angles are known to us.

Requirements: A ruler, a protractor and a compass.

Construction:

Let us consider a triangle ABC, whose perimeter is 15 cm and the two given angles be $55^{\circ}$ and $60^{\circ}$.

Thus A+B+C = 15 cm , $\angle B = 55^{\circ}$ $\angle C = 60^{\circ}$<

The steps for its construction are:

• Draw a line segment XY of length AB + AC + BC, that is, 15 cm.
• From the point X, using the protractor construct ∠LXY which is equal to ∠B, that is, 55°.
• From the point Y, construct ∠MYX which is equal to ∠C, that is, 60°.
• Using the compass, construct the bisectors of ∠LXY and ∠MYX. Mark the point as A where the constructors meet.

• Construct the perpendicular bisector of AX and name it as PQ.
• Construct the perpendicular bisector of AY and name it as RS.
• Let PQ meet XY at B and RS meet XY at C.
• Join the points A and B as well as A and C.

You get the ∆ABC of the required measurements.