Question

Construct a triangle with the same measurements given in above example taking PQ as base. Are the triangles congruent ?

Answer 1

PQ = 4 cm, QR = 5 cm. RP = 7cm.

Step -1 : 

Draw a rough sketch of the triangle and label it with the given measurements. 

Step – 2 : 

Draw a line segment PQ of length 4 cm.

Step – 3 : 

With centre P, drawn an arc of radius 7 cm. 

Step – 4 : 

Since R is at a distance of 5 cm from Q. draw another arc from Q with radius 5 cm such that it intersects first arc at R. 

Step – 5 : 

Join P, R and Q, R. 

The required APQR is constructed. The two triangles are congruent by Side – Side – Side (SSS) criterion for congruence.