Mid point theorem Application to solve Problems on Quadrilaterals

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

Learn in easy how to apply Mid point theorem to Problems based on Quadrilaterals

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 Q3-12:10

00:02 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 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.

12:10 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.

12:51 Proof

13:19 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.

14:30 Use property of parallelgram : Opposite angels are equal & Opposite sides are equal.

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