**Chapter 1 Geometrical Constructions Set 1.4**

Construct triangles of the measures given below:

Question 1.

In ∆SAT, l(AT) = 6.4 cm, m∠A = 45°, m∠T = 105°.

Solution:

Question 2.

In ∆MNP, l(NP) = 5.2 cm, m∠N = 70°, m∠P = 40°

Solution:

Question 3.

In ∆EFG, l(EG) = 6 cm, m∠F = 65°, m∠G = 45°.

Solution:

In ∆EFG,

m∠E + m∠F + m∠G = 180° …(sum of measures of angles of a triangle)

m∠E + 65° + 45° = 180°

m∠E + 110° = 180°

m∠E = 180° – 110°

m∠E = 70°

Question 4.

In ∆XYZ, l(XY) = 7.3 cm, m∠X = 34°, m∠Y = 95°.

Solution:

**Intext Questions and Activities**

Question 1.

In ∆ABC, m∠A = 60°, m∠B = 40°, l(AC) = 6 cm. (Textbook pg. no. 5)

1. Can you draw ∆ABC?

2. What further information is required before it can be drawn?

3. Which property can be used to get it?

4. Draw the rough figure to find out.

Solution:

1. ∆ABC cannot be drawn using the given information.

Seg AC is included inside the angles ∠A and ∠C. Since measure of ∠C is not known, the triangle cannot be drawn.

2. To draw the triangle, measure of ∠C is required.

3. The property of sum of the measures of the angles of a triangle can be used to find out m∠C.

4. In ∆ABC,

m∠A + m∠B + m∠C = 180°

∴ 60° + 40° + m∠C = 180°

∴ 100° + m∠C = 180°

m∠C = 180°- 100°

∴ m∠C = 80°