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Geometry

If a straight line intersects another two straight lines and if the alternate angles are equal to each other.

General Enunciation:If a straight line intersects another two straight lines and if the alternate angles are equal to each other.     Particular Enunciation: Let the straight line EF intersects AB and CD at G and H respectively so that ∠AGH= alternate ∠GHD and ∠BGH =alternate ∠GHC. It is required ...

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Solution of exercise 8.3(Circle)| Class Nine – Ten (9 – 10)| Part – 2

Problem – 4: The chords AB and CD of a circle with centre O meet at a right    angles at some points within the circle. Prove that ∠AOD +∠BOC=2 right angles.                                                                                                                                        General Enunciation: The chords AB and CD of a circle with centre O meet at right angles at ...

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Solution of exercise 8.2| Class Nine and Ten (9 – 10)

PROBLEM – 1. ABCD is quadrilateral inscribed in a circle with centre O. If the diagonals AC and BD intersect at the point E,prove that ∠AOB+∠COD=2∠AER.                                                                                                                                     General Enunciation: ABCD is quadrilateral inscribed in a circle with centre O. If the diagonals AC and BD intersect at the point E, ...

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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 ...

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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. ...

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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 ...

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