Question

Try to draw triangles with the following data. Can you draw these triangles. If not, look for the reason why you could not draw so.

i. ∆ABC in which m∠A = 85° , m∠B = 115° , l(AB) = 5cm.

ii. ∆PQR in which l(QR) = 2cm, l(PQ) = 4cm, l(PR) = 2cm.

Answer 1

i. m∠A + m∠B = 85° + 115° 

= 200°>180° 

But the sum of the measures of the angles of a triangle is 180° 

Hence, ∆ABC cannot be drawn.

ii. l(QR) + l(PR) = 2 cm + 2cm 

= 4 cm 

= l(PQ) 

But in a triangle, the sum of the length of any two sides of a triangle is always greater than the length of the third side. 

Hence, ∆PQR cannot be drawn.