Mid point theorem | Mid point theorem Application | Triangle Intercept Theorem

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

00:02 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q9 q1. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that :

(i) SR || AC and SR = 1/2AC (ii) PQ = SR (iii) PQRS is a parallelogram.

01:32 Proof

02:03 Application of Mid point theorem.Mid point theorem states that the line segment joining the mid-points of two sides of a triangle is parallel to the third side.

04:04 Apply property of parallelogram: Opposite sides are equal & Opposite angels are equal

04:20 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q9 Q2 ABCD is a rhombus and P, Q, R and S are ©wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

06:06 Proof

06:36 cosidrer similarity of triangles.

09:20 Apply Mid point theorem.Mid point theorem states that the line segment joining the mid-points of two sides of a triangle is parallel to the third side.

12:14 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q9 q3 ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

12:54 Proof

13:20 Concider two triangles and apply mid point theorem.Mid point theorem states that the line segment joining the mid-points of two sides of a triangle is parallel to the third side.

14:32 Use property of parallelgram : Opposite angels are equal & Opposite sides are equal.

16:32 q4 ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD.A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.

17:25 Proof

18:18 Use of converse of Mid point theorem.Mid point theorem states that the line segment joining the mid-points of two sides of a triangle is parallel to the third side.

19:25 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q9 q5 In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD.

20:45 APPLY property of parallelgram : Opposite angels are equal & Opposite sides are equal.

22:19 Here we learn how to collect relevant imformation to apply converce of Mid point theorem .Converce of Mid point theorem states that the line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side

24:28 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q9 q6 Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

26:15 Aim of so;ving problem

26:30 Analyse triangle to pull relevant imformation and apply converce of Mid point theorem.Converce of Mid point theorem states that the line draw

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CBSE solutions for class 9 maths Quadrilaterals

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Triangle Intercept theorem

Basic Proportionality Theorem

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