Question

Activity of maths verify experimently that the sum of a polygen is 360 degree do on assignment​

Answer 1

Answer

OBJECTIVE

To verify experimentally that the sum of the angles of a quadrilateral is 360°.

Materials Required

Cardboard

White paper

Tracing paper

Cutter/scissors

Coloured drawing sheets

Geometry box

Adhesive

Sketch pens

Prerequisite Knowledge

Concept of quadrilateral and its properties.

Theory

Quadrilateral: A closed figure having four sides, four angles and four vertices is called a quadrilateral.

Here, the term ‘Quad’ means ‘Four’ and term ‘Lateral’ means ‘Sides’, so that the term ‘Quadrilateral’ means ‘a figure bounded by four sides’.

In a quadrilateral ABCD, AB, BC, CD and DA are the four sides; A, B, C and D are the four vertices and ∠A, ∠B, ∠C and ∠D are the four angles formed at the vertices, (see Fig. 18.1).

NCERT Class 9 Maths Lab Manual - Verify that the Sum of the Angles of a Quadrilateral is 360° 1

Terms Related to Quadrilateral

Opposite Sides: Two sides of a quadrilateral which do not intersect, i.e. have no common end point (vertex) are called opposite sides. In quadrilateral ABCD, AB, CD and BC, AD are two pairs of opposite sides.

Consecutive or Adjacent Sides: Two sides of a quadrilateral which have a common point, i.e. intersect each other are called consecutive sides. In quadrilateral ABCD, AB, BC; BC, CD;

CD, DA and DA, AB are four pairs of consecutive sides.

Opposite Angles: Two angles of a quadrilateral are said to be opposite angles, if they do not have common arm. In quadrilateral ABCD, ∠A, ∠C and ∠B, ∠D are two pairs of opposite angles.

Consecutive or Adjacent Angles: Two angles of a quadrilateral are said to be consecutive or adjacent angles, if they have a common arm. In quadrilateral ABCD, ∠A, ∠B; ∠B, ∠C; ∠C, ∠D and ∠D, ∠A are four pairs of consecutive angles.

Diagonal: In a quadrilateral, the line segment joining the opposite vertices is called a diagonal of the quadrilateral. In quadrilateral ABCD, AC and BD are two diagonals.

The sum of the four angles of a quadrilateral is 360°.

Procedure

Take a piece of rectangular cardboard of suitable size and by using adhesive, paste a white paper on it.

Cut out a quadrilateral from a drawing sheet and name it as ABCD. Now, using adhesive, paste it on cardboard, (see Fig. 18.2).

NCERT Class 9 Maths Lab Manual - Verify that the Sum of the Angles of a Quadrilateral is 360° 2

Make cut outs of ∠A, ∠B, ∠C & ∠D of Quadrilateral ABCD with the help of tracing paper.(see in Fig.18.3).

NCERT Class 9 Maths Lab Manual - Verify that the Sum of the Angles of a Quadrilateral is 360° 3

Arrange the four cut out angles at a point O. (see Fig.18.4).

NCERT Class 9 Maths Lab Manual - Verify that the Sum of the Angles of a Quadrilateral is 360° .

Result

We have verified that the sum of the angles of a quadrilateral is a complete angle, i.e. 360°