The point and the lines| Basic Geometry
Point: A point has no length, breadth and thickness i.e., it has no magnitude. It has position only. It is regarded as an entity of zero dimensions. A point is always named with capital letters. Line:...
View ArticleTriangles| 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...
View ArticleThe 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...
View ArticleProve that a diagonal of a parallelogram divides it into two congruent...
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...
View ArticleProve that, if the opposite sides of a quadrilateral are equal and parallel,...
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...
View ArticleABC is an isosceles triangle and AB = AC. The side BC is extended up to D....
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 =...
View ArticleProve that the angle opposite the greatest side of a triangle is also the...
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....
View ArticleIn 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...
View ArticleIn 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...
View ArticleProve that the sum of the two diagonals of a quadrilateral is less than its...
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...
View ArticleProve 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...
View ArticleShow that of the two chords of a circle, the greater chord is nearer to the...
General enunciation: We have to show that of the two chords of a circle, the greater chord is nearer to the centre than the shorter. Particular enunciation: Let, O is the centre of the circle ABCD. AB...
View ArticleIf two equal chords of a circle intersect each other, show that two segments...
Problem: A chord AB one of the two concentric circles intersect the other circle at points C and D. Prove that AC = BD. General enunciation: A chord AB one of the two concentric circles intersect the...
View ArticleConcept of space, plane, line and point
Space: The space is the limitless three dimensional expanses where all matter exists. This is the region of near-vacuum surrounding all bodies in the universe. In geometry, we study geometric figures...
View ArticleSolutions of exercise 6.2| Class Nine – Ten(9-10)|Geometry
1.Define interior and exterior of an angle. The set of all points lying in the plane on the side C of AB and B side of AC is the interior region of the angle ∠BAC. The set of all points not lying in...
View ArticleCIRCLE| Part-1
Circle: The closed curved line at affixed distance from a fixed point is called circle. The fixed point is the centre of the circle and the fixed distance is called radius of the circle. In the...
View ArticleCircle| Part – 2
Exercise : Two chords AB and AC of a circle make circle make equal angles with the radius through A. Prove that AB=AC. Particular enunciation: Let O is the centre of the circle ABC. The two chords AB...
View ArticleClass Eight(8)-Circle-Exercise-10.1|Soltuion
Exercise-1: prove that, if two chords of a circle bisect each other , their point intersection will be the centre of the circle. General enunciation: We have to prove that, if two chords of a circle...
View ArticleCIRCLE | Part-3
Exercise: If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord. General enunciation: if two equal...
View ArticleSolution of Exercise- 10.2| Circle |Class- eight (8)
Exercise-1: If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord. General enunciation: if two equal...
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