Construction of Triangles

Step I: First, we draw a base line segment QR of the given length.

Step II: We cut two arcs with the given length from the points Q and R, so that they cut at a fixed point P.

Step III: We join points P and Q and points P and R to form the required isosceles triangle. ∆PQR has opposite sides equal. (PQ = PR)

Step I: We draw a base line segment NP of the given length.

Step II: We cut two arcs with given lengths from the points N and P, so that they intersect at point M.

Step III: Now, we join points M and N and points M and P to form the required scalene triangle. ∆ MNP has all the sides of different lengths.

Step I: First, we draw the base side LK of 5 cm.

Step II: Now, we form an angle L of 45° at the point L on the side LK with the help of a protractor.

Step III: Now we cut off the line segment LT of the length 3 cm from the side.

Step IV: We join points T and K to get the third side TK of the ∆ TLK.

So, ∆ TLK is the required angle.

Step I: First we draw the base side YZ of 4.5 cm.

Step II: Now we form an angle Y of 40° on point Y on YZ with the help of a protractor.

Step III: Similarly, we form an angle Z of 65° on point Z on YZ with the help of a protractor.

Step IV: The sides, other than the base side, intersect at a point X. We join points X and Y and X and Z to form the required ∆ XYZ.