Lab Manual: Verify that the Sum of the Angles of a Quadrilateral is 360° | Lab Manuals for Class 9 PDF Download

Objective

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).

• 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.

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).

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

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

Demonstration

• We came to know that the vertex of each cut out angle coincides at the point O.
• Such arrangement of cut outs indicates that the sum of the angles of a quadrilateral forms a complete angle, i.e. 360°.

Observation
Measures of ∠A = ………. ,
∠B = ………. ,
∠C = ………. ,
∠D = ………. ,
Sum of  ∠A + ∠B + ∠C + ∠D = ………. .

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

Application
This property may be useful in solving problems related to many types of quadrilaterals, such as parallelograms, trapeziums, rhombuses, squares and rectangles, etc.