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 ...

Read More »## Solution of exercise 8.4 (Circle) of class Nine and Ten ( 9 – 10)

Problem – 1. From some exterior point P of a circle with center O two tangents are drawn to the circle. Prove that OP is the perpendicular bisector of the chord of contact. Particular Enunciation: Given that, O and P are the centre and any exterior point respectively of the ...

Read More »## 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 ...

Read More »## Solution of exercise 8.3(Circle)| Class Nine – Ten (9 – 10)| Part – 1

Problem – 1: In the ∆ABC, if the bisectors of ∠B and ∠C meet the point P and their exterior bisectors at Q, show that the four points B, P, C and Q are concyclic. General Enunciation: In the ABC, if the bisectors of ∠B and ∠C meet the point ...

Read More »## 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, ...

Read More »## PDF| Solution of Exercise- 8.1(Circle) of class 9 and 10

PDF| Solution of Exercise: 8.1(Circle) of class 9 and 10 PDF file of Chapter 8.1: CLICK HERE Exercise 8.1 _Class – 9 and 10_ Problem – 1 : Prove that if two chords of a circle bisect each other, their point of intersection is the centre of the circle. ...

Read More »## Conditions of congruence of triangles

Definition of congruence: If two figures exactly cover each other then they are called congruent. Definition of congruence of triangles: If a triangle when placed on another, exactly covers the other, the triangles are congruent. Two triangles will be congruence if – Side Angle Side( SAS): If two pairs ...

Read More »## 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 ...

Read More »## 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. ...

Read More »## 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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