# NCERT Class 7 Mathematics Solutions: Chapter 10 – Practical Geometry Miscellaneous Exercise Part 1

1. Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and say why you cannot construct them. Construct rest of the triangle.

Triangle and its measures

1.

2.

3.

4.

5.

6.

7.

8.

In

Construction of is not possible because , and we know that the sum of angles of a triangle should be .

To construct: where .

Steps of construction:

(a) Draw a line segment .

(b) At point Q, draw with the help of compass.

(c) At point , draw with the help of compass.

(d) intersect at point .

We know that the sum of angles of a triangle is

To construct: where .

Steps of construction:

(a) Draw a line segment .

(b) At point , draw

(c) At point , draw

(d) intersect at point .

In

Construction of is not possible because, which forms a linear pair.

This is not possible to construct because the condition is

Sum of lengths of two sides of a triangle should be greater than the third side.

To construct: where .

Step of construction:

(a) Draw a line segment .

(b) Taking as centre and radius , draw an arc.

(c) Similarly, taking as centre and radius , draw an another arc which intersects the first arc at point .

To construct: A triangle whose are .

Step of construction:

(a) Draw a line segment .

(b) Taking as centre and radius , draw an arc.

(c) Taking as centre and radius , draw an another arc

(d) Both arcs intersect at point .