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Tuesday , August 22 2017

## Solution exercise 9.1| Class seven| Geometry

Problem-1: In the figure, ∆ABC is a triangle in which ∠ABC = 900, ∠BAC =480 and BD is perpendicular to AC. Find the remaining angles. Solution: Let remaining angles ∠ABD = x, ∠DBC = y and ∠BCD = z. Since BD⊥AC ∴ ∠ADB = ∠CDB = 900 Now, in ∆ABD ...

## Prove that opposite angles of a quadrilateral are equal to each other then it is a parallelogram

Problem: Prove that opposite angles of a quadrilateral are equal to each other then it is a parallelogram. General enunciation: we have to prove that, if opposite angles of a quadrilateral are equal to each other then it is a parallelogram. Particular enunciation: Let ABCD is a quadrilateral. Here ∠B=∠D ...

## Prove that, summation of four angles of a quadrilateral is equal to four right angles.

Ex: In the figure, ABC is an equilateral triangle. D, E and the midpoint of AB,BC and AC respectively.            (a) Prove that, summation of four angles of a quadrilaterals equal to four right angles. Prove that, ∠BDF+∠DFE+∠FEB+∠EBD= 4 right angles.      (b) Prove that, DF∥BC and DF = ½ BC. ...

## Prove that, if the opposite sides of a quadrilateral are equal and parallel, it is a parallelogram

Exercise: Prove that, if the opposite sides of a quadrilateral are equal and parallel, it is a parallelogram. General enunciation: We have to prove that if the opposite sides of a quadrilateral are equal and parallel, it is a parallelogram. Particular enunciation: Let the opposite sides of the quadrilateral ABCD ...

## Solution of the activity| Quadrilaterals| Class eight(8)

Quadrilaterals: A quadrilateral is a closed figure bounded by four line segments. Type of Quadrilaterals: Parallelogram: A parallelogram is a quadrilateral with opposite sides parallel. The region bounded by a parallelogram is also known as parallelogram. Rectangle: A rectangle is a parallelogram with a right angle .The region bounded by ...

## In the quadrilateral ABCD, AB = CD, BC = CD and CD>AD. Prove that ∠DAB > ∠BCD

Solution: General enunciation: In the quadrilateral ABCD, AB = CD, BC = CD and CD>AD. Prove that ∠DAB > ∠BCD. Particular enunciation: Given that, In the quadrilateral ABCD, AB = CD, BC = CD and CD>AD. We have to proved that ∠DAB > ∠BCD. Construction: We join A and C. ...

## Prove that if two chords of a circle bisect each other, their point of intersection is the centre of the circle.

General enunciation: If two chords of a circle bisect each other, we have to show that their point of intersection is the centre of the circle. Particular enunciation: Suppose two chords AC and BD of the circle ABCD bisect each other at the point O i.e., OA = OC and ...

## Prove that, if the diagonals of a quadrilateral bisect each other, it is a parallelogram.

Solution: General enunciation: To prove that if the diagonals of a quadrilateral bisect each other, it is a parallelogram. Particular enunciation: Let the diagonals AC and BD of the quadrilateral ABCD bisect each other at O. We have to prove that ABCD is a parallelogram. Proof: The diagonals AC and ...