Solution of the activity| Quadrilaterals| Class eight(8)
Quadrilaterals: A quadrilateral is a closed figure bounded by four line segments. Type of Quadrilaterals: Parallelogram: A parallelogram is a quadrilateral with opposite sides parallel. The region...
View ArticleProve that, if the opposite sides of a quadrilateral are equal and parallel,...
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...
View ArticleProve that, summation of four angles of a quadrilateral is equal to four...
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...
View ArticleProve that opposite angles of a quadrilateral are equal to each other then it...
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...
View ArticleConditions 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,...
View ArticlePDF| 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,...
View ArticleSolution 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....
View ArticleSolution 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...
View ArticleSolution 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....
View ArticleSolution 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:...
View ArticleIf a straight line intersects another two straight lines and if the alternate...
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...
View ArticleThe straight lines which are parallel to the same straight line are parallel...
Theorem: If a straight line intersects another two straight lines and if the corresponding angles are equal to each other. General enunciation: If a straight line intersects another two straight lines...
View ArticleIf three sides of a triangle are respectively equal to the corresponding...
General enunciation: If three sides of a triangle are respectively equal to the corresponding three sides of another triangle, then the triangle are congruent. Particular enunciation: Let, in ∆ABC...
View ArticleIf two sides of a triangle are equal, then the angles opposite the equal...
General enunciation: If two triangles have two sides of the one equal to two sides of the other, each to each, the angles included by those sides are also equal then the triangles are equal in all...
View ArticleSolution of exercise 9.2(Triangle)| Class seven
Problem-9: In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC. Particular enunciation: Given that, in the triangle ABC, AB>AC and the...
View ArticleIf two angles of triangles are equal, then the sides opposite to the equal...
If two angles of triangles are equal, then the sides opposite to the equal angles are equal. Particular enunciation: Let ABC be a triangle in which the ∠ACB = the ∠ABC. We have to prove that AB =AC....
View ArticleIf two triangles have the three sides of the one equal to the three sides of...
If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects. Particular enunciation: In the ∆ABC and ∆DEF, AB = DE, AC =...
View ArticleExercise 10.1|Class seven| Congruence| Part – 1
Problem – 1: In the figure, CD is the perpendicular bisector of AB, Prove that ∆ADC ≅ ∆BDC. Solution: Particular enunciation: Given that, in the figure, CD is the perpendicular bisector of AB. i.e., AD...
View ArticleSolution exercise 9.1| Class seven| Geometry
Problem-1: In the figure, ∆ABC is a triangle in which ∠ABC = 900, ∠BAC =480 and BD is perpendicular to AC. Find the remaining angles. Solution: Let remaining angles ∠ABD = x, ∠DBC = y and ∠BCD = z....
View ArticleExercise 10.1|Class seven| Congruence| Part – 2
Problem – 5: In the figure, AD = AE, BD = CE and ∠AEC = ∠ADB. Prove that AB = AC. Particular enunciation: In the figure, AD = AE, BD = CE and ∠AEC = ∠ADB. We have to prove that AB = AC. Proof: In ∆ACE...
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