NCERT Class 9 Maths Lab Manual – Verify that the Sum of the Angles of a Quadrilateral is 360°
To verify experimentally that the sum of the angles of a quadrilateral is 360°.
- White paper
- Tracing paper
- Coloured drawing sheets
- Geometry box
- Sketch pens
Concept of quadrilateral and its properties.
- 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.
- The sum of the four angles of a quadrilateral is 360°.
- 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).
- 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°.
Measures of ∠A = ………. ,
∠B = ………. ,
∠C = ………. ,
∠D = ………. ,
Sum of ∠A + ∠B + ∠C + ∠D = ………. .
We have verified that the sum of the angles of a quadrilateral is a complete angle, i.e. 360°.
This property may be useful in solving problems related to many types of quadrilaterals, such as parallelograms, trapeziums, rhombuses, squares and rectangles, etc.
What is the angle sum property of a quadrilateral?
The sum of all angles of a quadrilateral is a complete angle, i.e. 360°.
The sum of three angles of a quadrilateral is 280°. Find the measure of the fourth angle.
Fourth angle = 360° – 280° = 80°
Is it true that every parallelogram is a rectangle?
No, only those parallelogram is a rectangle whose all angles are 90°.
In which quadrilateral(s), diagonals are perpendicular to each other?
Is it true that diagonals of a rhombus are equal?
What are the conditions that any quadrilateral be a square?
- All four sides of a quadrilateral are equal.
- Each angle of a quadrilateral is 90°.
- Diagonals are equal and bisect each other.
Is it true that parallelogram is always a trapezium but a trapezium is not always a parallelogram?
How many vertices a quadrilateral has?
A quadrilateral has 4 vertices.
Can all the angles of a quadrilateral be right angles? Give reason.
Yes, all the angles of a quadrilateral can be right angles, e.g. Square and rectangle.
Verify experimentally the angle sum property for other types quadrilateral.