**Chapter 10 Practical Geometry Exercise 10.4**

Question 1.

Construct ∆ABC, given m ∠A = 60°, m ∠B = 30° and AB = 5.8 cm.

Solution:

Steps of construction:

(i) Draw AB = 5.8 cm.

(ii) Draw ∠A = 60° and ∠B = 30° to meet each other at C.

(iii) ABC is the required triangle.

Using ASA criterion

Question 2.

Construct ∆PQR if PQ = 5 cm, m ∠PQR = 105° and m∠QRP = 40°.

(Hint: Recall angle-sum property of a triangle)

Solution:

Given: m∠PQR = 40°, m∠QRP = 105°

∵ m∠PQR + m∠QRP + ∠QPR = 180° (Angle sum property of a triangle)

105° + 40° + ∠QPR = 180°

145° + ∠QPR = 180°

∴ ∠QPR = 180° – 145° = 35°

Steps of construction:

(i) Draw PQ = 5 cm.

(ii) Draw ∠QPR = 35° and ∠PQR = 40° to meet each other at R.

(iii) ∆PQR is the required triangle.

[Using AAS or ASA criterion]

Question 3.

Examine whether you can construct ∆DEF such that EF = 7.2 cm, m∠E = 110° and m∠F = 80°. Justify your answer.

Solution:

To construct ∆DEF with the given measurement, is not possible.

∵ m∠E + m∠F = 110° + 80°

= 190° > 180° [Sum of the angles of a triangle = 180°]

∴ ADEF is not possible to construct.