Parallelograms on the same Base and Between the same Parallels

http://www.learncbse.in/ncert-solutions-for-class-9-maths/

In this chapter, we will study more about Parallelogram Theorems based on Areas of Parallelograms and Triangles, their properties and especially those of Areas of Parallelograms.

In this video, we learn how to apply Congruency Rule to solve Problems on Areas of Parallelograms and Triangles. Use parallel lines concept and triangle congruence theorems to prove/solve problems on Areas of Parallelograms and Triangles.

00:02 CBSE Class 9 maths solutions Areas of Parallelograms and Triangles Q1. In Fig. 9.15, ABCD is a parallelogram, AE perpendicular DC and CF perpendicular AD.If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

00:37 Use properties of parallelogram:In a parallelogram, pair of opposite sides are equal & Opposite angels are equal.

01:26 Apply Area of Parallelogram Formula:Area of a parallelogram is the product of its base and the corresponding altitude.

02:00 Find Area of a parallelogram with base CD

02:40 Find Area of a parallelogram with base AD

03:33 CBSE Class 9 maths solutions Areas of Parallelograms and Triangles Q2. If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, show thatar (EFGH) = 1/2 ar (ABCD) .

04:20 Construction Procedure to solve the given Word Problem

04:33 Use properties of parallelogram:In a parallelogram, pair of opposite sides are equal & Opposite angels are equal.

05:30 Apply Parallelogram Theorem: If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.

07:38 Adding the obtained results.

09:01 CBSE Class 9 maths solutions Areas of Parallelograms and Triangles Q3. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).

09:40 Construction Procedure to solve the given Word Problem

10:50 Apply Area of Triangle Formula:Area of a triangle is half the product of its base and the corresponding altitude.

12:42 CBSE Class 9 maths solutions Areas of Parallelograms and Triangles Q4. In Fig. 9.16, P is a point in the interior of a parallelogram ABCD. Show that

(i) ar (APB) + ar (PCD) = 1/2 ar (ABCD) (ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD) [ Hint : Through P, draw a line parallel to AB.]

13:28 Construction

14:30 Apply Parallelogram Theorem:If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram

17:30 (ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD)

19:12 use Parallelogram Theorem

22:35 CBSE Class 9 maths solutions Areas of Parallelograms and Triangles Q5. In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that

(i) ar (PQRS) = ar (ABRS) (ii) ar (AX S) = 1/2 ar (PQRS)

24:40 Apply Parallelogram Theorem:Parallelograms on the same base (or equal bases) and between the same parallels are equal in area.

26:40 CBSE Class 9 maths solutions Areas of Parallelograms and Triangles Q6.A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?.

27:34 Construction to solve the given Word Problem

28:45 Apply Parallelogram Theorem: If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.

29:16 Apply AREA Axoim:If a planar region formed by a figure T is made up of two non-overlapping planar regions formed by figures P and Q, then ar (T) = ar (P) + ar (Q), where ar (X) denotes the area of figure X.

Basic Concept:

Area of a parallelogram is the product of its base and the corresponding altitude.

Area of a triangle is half the product of its base and the corresponding altitude.

Paralleogram Theorem:

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

Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallels.

Reference book for the above video is

National Council of Educational Research and Training (NCERT) Book for Class 9 Subject: Maths

This Video is also refers as CBSE Class 9 mathts NCERT Solutions Chapter 9 Areas of Parallelograms and Triangles

This video is suited for CBSE class 9 maths Areas of Parallelograms and Triangles.

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