Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 10 Practical Geometry Ex 10.4 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 7 Maths Chapter 10 Practical Geometry Ex 10.4

Question 1.

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

Solution:

Steps of construction:

I. Draw a line segment AB = 5.8 cm.

II. Construct ∠BAX = 60° at A.

III. At B, construct ∠ABY = 30°.

IV. Let the rays AX and BY intersect at C.

Thus, ∆ABC is the required triangle.

Question 2.

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

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

Solution:

Here the line segment PQ is given. We can construct the triangle, if the measure of ∠QPR is known.

Here, ∠QPR = 180° – [∠PQR + ∠QRP]

= 180° – [105° + 40°]

= 180° – [145°] = 35°

Steps of construction:

I. Draw a line segment PQ = 5 cm.

II. At P, construct ∠QPX = 35°.

III. At Q, construct ∠PQY = 105°.

IV. Let the rays \(\overrightarrow{\mathrm{PX}}\) and \(\overrightarrow{\mathrm{QY}}\) intersect at R.

Thus, ∆PQR is the required triangle.

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:

Here, m∠E = 110° and m∠F = 80°.

i.e., m∠E + m∠F = 110° + 80° = 190° > 180°. Since, sum of the three angles of a triangle is 180°.

∴ The ADEF is not possible, having sum of two angles > 180°.

Thus, ∆DEF cannot be constructed.