EducatorSharmin

 Triangles, Quadrilateral & Polygons: Chapter-11 Triangles: Classification of Triangles: 1. Equilateral Triangle: A triangle with 3 equal sides 2. Isosceles triangle:  A triangle with at least 2 equal sides 3. Scalene triangle: A triangle with no equal sides * The sum of interior angles of a triangle is 180⁰  * An exterior angle of a triangle is equal to the sum of its interior opposite angles. Q. 1. a) In the figure, ABD is a straight line. Calculate the value of a. Solution:  a) a⁰  = 56⁰  + 50⁰ (ext. ∠ of △) = 106⁰ a = 106 b) In the figure, ACE, BCD and DEF are straight lines. Calculate the value of b and of c.             b) ACB = 94⁰ (vert. opp. ∠s)  b⁰  +  38⁰  + 94⁰ = 180⁰ ( ∠sum of  △ ABC)                    b⁰ = 180⁰  -  38⁰  - 94⁰ = 48⁰       c⁰  = 25⁰  + 94⁰             ...

Pythagorean Theorem One of the most famous theorems in mathematics is the Pythagorean Theorem , named for the Ancient Greek mathematician Pythagoras. This theorem can be used to find information about the lengths of the sides of a right triangle.  Real Life Applications: Building and architecture Navigation and GPS Games and sports What other examples can you think of for using the Pythagorean Theorem in your life? Q. Who discovered this theorem? Pythagoras was an ancient Greek philosopher and mathematician, born around 570 BCE on the island of Samos in the eastern Aegean Sea. Pythagoras founded a religious and philosophical school in Croton (now Crotone) in southern Italy, known as the Pythagorean school . Pythagoras and his followers made significant contributions to mathematics , including discoveries in geometry, arithmetic, and number theory. The ancient Greek mathematician and philosopher Pythagoras is credited with discovering this relationship in the 6th century BCE due ...

Perpendicular Bisectors: A perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.  Properties of a Perpendicular Bisector: It divides AB into two equal halves or bisects it. It makes right angles with (or is perpendicular to) AB. Every point in the perpendicular bisector is equidistant from points A and B. While working with practical geometry, we will often find the application  of perpendicular bisectors; say when we are asked to draw an isosceles  triangle, or when we have to determine the centre of a circle, etc.  Below are the steps to construct a perpendicular bisector of a line  using a compass and a ruler. Q.1. Draw a line segment AB of length 10 cm. Construct the perpendicular bisector of AB. Solution: Construction Steps: 1. Using a ruler, draw a line segment AB of length 10 cm. 2. Adjust the arms of the compasses so that the distance between the ends is more than ha...