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

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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.

Answer: (1)

In

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

Answer: (2)

To construct: where .

Steps of construction:

(a) Draw a line segment .

A Line Segment QR= 4.7 Cm

A line segment QR= 4.7 cm

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

At Point Q, Triangle XQR=30 Degree

At point Q, triangle XQR=30 degree

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

At Point R, Draw ∆YRQ = 60 Degree

At point R, draw ∆YRQ = 60 degree

(d) intersect at point .

QX and RY Intersect at Point P

QX and RY intersect at point P

Answer: (3)

We know that the sum of angles of a triangle is

To construct: where .

Steps of construction:

(a) Draw a line segment .

A Line Segment AC=3 Cm

A line segment AC=3 cm

(b) At point , draw

At Point C, Triangle YCA =60 Degree

At point C, triangle YCA =60 degree

(c) At point , draw

At Point a, Draw ∆XAC = 70 Degree

At point R, draw ∆XAC = 70 degree

(d) intersect at point .

XA and YC Intersect at Point B

XA and YC intersect at point B

Answer: (4)

In

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

Answer: (5)

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.

Answer: (6)

To construct: where .

Step of construction:

(a) Draw a line segment .

A Line Segment QR=4 Cm

A line segment QR=4 cm

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

Q as a Center and Radius 3.5 Cm

Q as a center and radius 3.5 cm

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

R as a Center and Radius 3.5 Cm

Q as a center and radius 3.5 cm intersects the first arc at point P

Answer: (7)

To construct: A triangle whose are .

Step of construction:

(a) Draw a line segment .

A Line Segment ZY=4 Cm

A line segment ZY=4 cm

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

Z as a Center and Radius 5 Cm

Z as a center and radius 5 cm

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

Y as a Center and Radius 3 Cm

Q as a center and radius 3 cm

(d) Both arcs intersect at point .

Both Arc Intersect at Point X

Both arc intersect at point X

Answer: (8)

To construct: A triangle DEF whose are .

Step of construction:

(a) Draw a line segment

A Line Segment EF = 5.5 Cm

A line segment EF = 5.5 cm

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

E as a Center and Radius 4.5 Cm

E as a center and radius 4.5 cm

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

F as a Center and Radius 4 Cm

Q as a center and radius 3 cm, an another arc which intersects the first arc at point D