cbse-class-9-median-of-a-triangle-divides-it-into-two-triangles-of-equal-areas-word-problems

CBSE Class 9| Median of a triangle divides it into two triangles of equal areas | Word Problems

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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.

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.

Two figures are said to be on the same base and 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.

00:02 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q1. In Fig.9.23, E is any point o.n median AD of a Triangle ABC. Show that ar (ABE) = ar (ACE).

00:30 Defination of Median : A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side

01:06 Apply Area of triangle formula:Area of a triangle is the product of its base and the corresponding altitude.

03:18 Apply Area Axiom: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)

05:25 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q2. In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = 1/4 ar(ABC)

06:23 Median:A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side

06:38 Apply Area Theorem:A median of a triangle divides it into two triangles of equal areas.

08:20 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q3. Show that the diagonals of a parallelogram divide it into four triangles of equal area.

09:55 Median of Triangle

09:59 A median of a triangle divides it into two triangles of equal areas.

23:36 Q4. In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that ar(ABC) = ar (ABD).

13:46 A median of a triangle divides it into two triangles of equal areas.

15:36 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q5. D, E and F are respectively the mid-points of the sides BC, CA and AB of a Triangle ABC. Show that (i) BDEF is a parallelogram. (ii) ar (DEF) = 1/4 ar (ABC) (iii) ar (BDEF) = 1/2 ar (ABC).

17:47 Apply Mid point Theorem:The line-segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it.

19:38 Use Properties of Parallelogram:In a parallelogram, pair of opposite sides are equal & Opposite angels are equal.

20:07 (ii)

26:04 Adding two results to get the desired results

29:21 Apply properties of paralleogram:Diagonals of a parallelogram bisect each other at right angles

24:08 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q6. In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that: (i) ar (DOC) = ar (AOB) (ii) ar (DCB) = ar (ACB) (iii) DA || CB or ABCD is a parallelogram. [ Hint : From D and B, draw perpendiculars to AC.]

27:00 Apply area of triangle

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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CBSE solutions for class 9 maths Areas of Parallelograms and Triangles

CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles

CBSE class 9 maths NCERT Solutions chapter 10 Areas of Parallelograms and Triangles

Solutions for CBSE Class 9 Maths Chapter 10

NCERT solutions for class 9 maths Areas of Parallelograms and Triangles

NCERT solutions for CBSE class 9 maths Areas of Parallelograms and Triangles

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