Notes For Areas Of Parallelograms And Triangles Class 9 Formulas Download PDF

Chapter 9 Areas of Parallelograms and Triangles ncert Soluiions algebra area of parallelogram volume of cone books

INTRODUCTION

You may recall that the part of the plane enclosed by a simple figure is called a planar region
corresponding to that figure. The magnitude or measure of this lanar region is called its area.

We are also familiar with the concept of congruent figures.

Two figures are called congruent, if they have the same shape and the same size.

So if two figures A and B are congruent they must have equal areas. However, the converse of
this statement is not true. In other words, two figures having equal areas need not be congruent.
For example, in figure, rectangles ABCD and EFGH have equal areas (9 x 4 cm2 and 6 x 6
cm2) but clearly they are not congruent.

Two figures are said to be on the same â€˜base add between the same parallels, if they have a
common base (side) and the vertices (or the vertex) opposite to the common base of each figure
lie on a line parallel to the base.

If a parallelogram PQRS, a rectangle EFGH and a triangle LMN are so drawn that their bases
lie on a straight line (say, CD) and their other vertices lie on a line AB parallel to it (CD), then
the parallelogram, the rectangle and the triangle are said to be between the same parallels.

**Note :** Out of the two parallels, one must be the line containing the common base. Î”ABC and
Î”DBE of figure are not on the common base.

PARALLELOGRAMS ON THE SAME BASE AND BETWEEN THE SAME PARALLELS.

**Statement : **Parallelograms on the same base and between the same parallels are equal in area.

**Remark: **Area of a parallelogram is the product of its any side and the corresponding altitude.

**Statement :** if a triangle an a a parallelog Ain Are mit* same base and between the same
parallels, then the area of the triangle is equal to half the area of the parallelogram.

TRIANGLES ON THE SAME BASE AND BETWEEN THE SAME PARALLELS

Two triangles on the same base (or equal bases) and between the same parallels are equal in
area.

**Note :** Area of Î”ADC = 1/2 x base DC x corresponding altitude AN

In other words, area of a triangle is half the product of its base (or any side) and the
corresponding altitude (or height).

**Remarks : **Two triangles with same base (or equal bases) and equal areas will have equal
corresponding altitudes.

**Theorem : **Two triangles having the same base (or equal bases) and equal areas lie between the
same parallels.

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- Chapter 1 NUMBER SYSTEMS
- Chapter 2 POLYNOMIALS
- Chapter 3 COORDINATE GEOMETRY
- Chapter 5 INTRODUCTION TO EUCLIDâ€™S GEOMETRY
- Chapter 6 LINES AND ANGLES
- Chapter 7 TRIANGLES
- Chapter 12 HERONâ€™S FORMULA
- Chapter 4 Equations In Two Variables
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 13 Volume and Surface Area
- chapter 14 Statistics
- Chapter 15 Probability
- Chapter 11: Constructions

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