Triangle Construction: Given its Perimeter and Two Angles

A triangle is a closed two-dimensional figure with three sides. There are different ways to construct a triangle. If the three sides are given, we can easily construct a triangle. Here, we are going to discuss how to construct a triangle when its perimeter and its two angles are given.

How to Construct a Triangle When its perimeter and Two Angles are Given?

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

Requirements: A ruler, a protractor and a compass.


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.

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