BIGtheme.net http://bigtheme.net/ecommerce/opencart OpenCart Templates
Tuesday , August 22 2017
Home / Geometry (page 4)

Geometry

Prove that the middle points of equal chords of a circle are concyclic.

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 ...

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, ...

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 = ...

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 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 ...

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 ...

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. ...

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: ...