mid-point-theorem-triangle-intercept-theorem-applications

Mid point theorem | Triangle Intercept Theorem | Applications

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

In this video, we have 6 solutions .All these solutions are based on geomentry properties of triangles and intended to use Mid point theorem and its converse.Students can learn to solve problems on Mid point theorem and converse of Mid point theorem. Q1-00:02 Q2-04:22 Q3-12:12 Q5-16:30 Q6-21:33 Q7-25:45

00:02 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals 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.

01:33 Proof

02:02 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.

04:05 Apply property of parallelogram: Opposite sides are equal & Opposite angels are equal

04:22 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals 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.

06:04 Proof

06:37 cosidrer similarity of triangles.

09:21 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.

12:12 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals 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.

12:55 Proof

13:22 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.

14:33 Use property of parallelgram : Opposite angels are equal & Opposite sides are equal.

16:30 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals 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.

17:51 APPLY property of parallelgram : Opposite angels are equal & Opposite sides are equal.

18:48 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

19:58 Apply converce of Mid point theorem

21:33 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q6 Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

22:45 Aim of solving problem

23:40 Analyse triangle to pull relevant imformation and 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

24:45 Use Mid point theorem

25:22 From property of Parallelogram : Opposite angels are equal & Opposite sides are equal.

25:45 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q7 ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that

(i) D is the mid-point of AC (ii) MD Perpendicular to AC (iii) CM = MA = 1/2AB

27:42 Aim of solving problem

27:55 Learn procedure to extract imformation which helps to use appropriate theorem

29:21 Use parallines theorem and apply property of co interior angles

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