SSS, SAS, ASA, AAS and RHS – Congruence of Triangles In geometry we see that, if two line segments are are same in length, they are congruent, and if two angles are same in measure they are also congruent,.Simply, we can say congruent means an object and its mirror image. Congruence Triangles A triangle is a polygon with […]
Read More →Theorem The perpendicular from the center of a circle to a chord bisects the chord. Given: A circle with center O, AB is chord of a circle and OC perpendicular from the center to the chord AB. i.e. OC ⊥ AB therefore ∠OCA and ∠OCB Both angles are 900. To prove: AC = CB (C is the mid point of chord AB) […]
Read More →How to calculate the volume of a cube with examples A cube is a solid box of six square faces, all of which sides have equal in length and every square is same in area. A cube has, (1) Six surfaces (2) Eight vertices (3) Twelve edges or sides of equal length Volume of a […]
Read More →The perpendicular from the center of a circle to a chord bisects the chord. Given: A circle with center O, AB is chord of a circle and OC perpendicular from the center O to the chord AB. i.e. OC ⊥ AB therefore ∠OCA and ∠OCB, Both angles are 900. To prove: AC = CB Construction: join OA and OB. Proof: In △OCA and △ OCB ∠OCA = ∠OCB […]
Read More →If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Given: ABCD is a quadrilateral, each pair of opposite sides of quadrilateral ABCD are AB and CD and also sides AD and BC are equal. AB = CD BC = AD To prove: ABCD is a parallelogram. Construction: Join A to C that is AC, is […]
Read More →Types of triangles- Right, Acute, Obtuse….. Type on triangles on base of angles 1. Right triangle: If in a triangle, one angle is 90 degree, the triangle called right triangle. or A right triangle has a 900 angle. The following triangle is a right triangle. 2. Acute triangle: If in a triangle, all three […]
Read More →Triangle – Definition and Properties The origin of term “Triangle” from latin word tri (“Three”) and angulus means (“angles”). A “Triangle” is a simple closed curve or a three sided polygon. A triangle has three angles and three sides and three vertices. It is one of the basic shape in geometry. In Euclidean geometry any non-collinear, three points, determine a unique triangle. The triangle […]
Read More →Vertically Opposite Angles Theorem Vertical angles theorem or Vertically opposite angles theorem states that, If two lines intersect each other, then vertically opposite angles are equal. Given: In the above statement, given that two lines intersect each other, so let AB and CD are two lines intersect each other at O as shown in figure so […]
Read More →Law of cosines or Cos law The law of cosines or Cos law is one of the trigonometric laws which is useful for solving the angles or sides of a triangle. For example, if all three sides of a triangle (SSS) are given, the cosine rule allows one to easily find any of the […]
Read More →Hypotenuse of a triangle In geometry, the longest side of a right-angled triangle, the side opposite the right angle is known as hypotenuse. Pythagoras theorem applies to right triangles and states that, The square on the hypotenuse is equal to the sum of the squares on the other two sides. (hypotenuse)2 = (Base)2+(Perpendicular)2 […]
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