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 […]
Read More →Law of sines or Sine law The law of sines or Sine law is one of the trigonometric laws which is useful for solving the angles or sides of a triangle. In trigonometry, the law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite […]
Read More →Square – Properties – Formula Here we will learn, about some geometrical properties of a square. In below figure ABCD is a square. Properties of a square 1. All four sides of a square are equal or congruent. 1. All four sides of a square are equal or congruent. AB = BC = CD = DA 2. All […]
Read More →Solutions of Trigonometric Ratios (1) If sin A = 4/5, find the other trigonometric ratios of the angle A. Solution: Let us draw a right △ ABC in which ∠B = 900 We know that, sin A = 4/5 = BC/AC Therefore, if BC =4k, then AC = 5k, where k is a positive number. Now, using […]
Read More →Common Geometry Symbols Geometry Symbol Symbol Symbol Name (1) ∠ Angle (2) ∟ Right angle (3) ∡ […]
Read More →Vertex – Definition and Examples Vertex – Latin word Vertex meaning, “highest point”. What is Vertex? Vertex is a point where two or more rays or line segments are meet. When two rays or line segments meet, simply it is a corner, they form an angle. Definition: A vertex is a point on a polygon, where […]
Read More →Trigonometric ratios in right triangles In a triangle, if any one angle is a right angle ( that is a 90 degree angle) then the triangle is called right triangle. A triangle has three sides, the longest side of the triangle is opposite of right angle called Hypotenuse, and the other two sides including the right […]
Read More →Angle – Angle – Similarity If two angles of a triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Given: Two △ABC and △PQR such that ∠B = ∠Q, and ∠C = ∠R To prove: △ABC ~ △PQR Proof: In △ABC, ∠A + ∠B +∠C = 1800….(1) by angle sum property In △PQR∠P + […]
Read More →AAS Congruence Rule Angle-Angle-Side Two triangles are congruent, if two pairs of corresponding angles and one pair of opposite sides are equal in both triangles. In above figure there are two triangles, △CAB and △PQR △CAB and △PQR has two pairs of corresponding angles ∠A = ∠R, ∠C = ∠P and one pair of opposite sides side CB = side PQ. […]
Read More →2D – Shapes – Definition – Properties Here is a detailed explanation of common 2D shapes, including their definitions, examples, diagrams, and properties: Definition: 2D shapes are flat and also known as plane shapes, ‘2D’ stands for 2-dimensional. These shapes can be drawn on paper and have length and width. We can measure length and […]
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