General enunciation: We have to show that the middle points of equal chords of a circle are concyclic. Particular enunciation: Consider, O is the centre of the circle ABCD, AB, CD and EF are three equal chords of it. M, N and P are the middle points of AB, CD ...

Read More »## Prove that the sum of the two diagonals of a quadrilateral is less than its perimeter

General enunciation: We have to prove that the sum of the two diagonals of a quadrilateral is less than its perimeter. Particular enunciation: Let, AC and BD are the two diagonals od ABCD quadrilateral. Prove that AC + BD < AB + BC + CD + AD Proof: ∆ ABC, ...

Read More »## In the figure, PM⊥QR, ∠QPM = ∠RPM and ∠QPR =900.

(a) Find the measure of ∠QPM. (b) What are the measure of ∠PQM and ∠PRM? (c) If PQ = 6 cm. Find the measure of PR. Solution: Given that, PM⊥QR, ∠QPM = ∠RPM and ∠QPR =900. (a) ∠QPM + ∠RPM = ∠QPR ⟹∠QPM + ∠QPM = ∠QPR [∵∠QPM = ...

Read More »## 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. ...

Read More »## Prove that the angle opposite the greatest side of a triangle is also the greatest angle of that triangle.

Problem: Prove that the hypotenuse of a right angled triangle is the greatest side. Solution: General enunciation: We have to prove that the hypotenuse of a right angled triangle is the greatest side. Particular enunciation: Let ∆ABC be right angled triangle in which ∠ABC = right angle or 900 and ...

Read More »## ABC is an isosceles triangle and AB = AC. The side BC is extended up to D. Prove that AD>AB.

Solution: General enunciation: ABC is an isosceles triangle and AB = AC. The side BC is extended up to D. Prove that AD>AB. Particular enunciation: Given that, ABC is an isosceles triangle and AB = AC. The side BC is extended up to D. It is required to prove that ...

Read More »## 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 are equal and parallel i.e., BC = AD, BC || AD and AB = CD, AB || CD. ...

Read More »## Prove that a diagonal of a parallelogram divides it into two congruent triangles.

General enunciation: We have to prove that a diagonal of a parallelogram divides it into two congruent triangles. Particular enunciation: Let the diagonal of the parallelogram ABCD is BD. The diagonal BD divides the parallelogram into two triangles ABD and BCD. We have to prove that ∆ABD ≅ ∆BCD Proof: ...

Read More »## The angles| Geometry

Angle: An angle is a figure formed by two rays with a common end point. The common end point is called the vertex of the angle and the rays are called sides of the angle Acute angle: An acute angle is an angle whose measure is greater than 00, but ...

Read More »## Triangles| Geometry

Definition: The figure bounded by three line segments is a triangle .The line segments are known as the sides of the triangle. The point common to any two sides is known as vertex. The angle formed at the vertex is an angle of the triangle. The triangle has three sides ...

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