Parallelograms – Properties   A parallelogram is a special type of a polygon. it is a quadrilateral with both pair of opposite sides are parallel. Properties 1. Opposite sides are equal.       Opposite sides, AB = CD and AC = BD 2. Opposite angles are equal.      Opposite angles are ∠A = ∠D and ∠B […]

Read More →

Given: Two triangles △ ABC and △ ABD are on same base (or equal bases) AB, and area of △ ABC and △ ABD are equal. Proof: CD ∥ AB Construction: Draw CE and DF perpendicular to AB.So DF is the height of △ ADB, and CE is the height of △ABC. CE perpendicular to AB and DF perpendicular to AB.Since, lines perpendicular to same line […]

Read More →

Two triangles on the same base (or equal bases) and between the same parallels are equal in area. Given: △ ABC and △ PBC are two triangles on same base (or equal bases) BC and between the same parallels, BC and AP. To prove: ar △ ABC = ar △ PBC Construction: Through B, draw BD ∥ CA intersecting PA produced at D, and […]

Read More →

Intersection of sets  Definition: The ‘Intersection of two sets’ A and B is the set of all elements, which belong to both A and B. or simply,  The ‘Intersection of two sets’ A and B is the set of all elements, which are common in both A and B. Symbol  ‘∩’ is used to denoted the Intersection of two sets […]

Read More →

Union of Sets – Set Operations In this tutorial we will learn, properties of operation of union of sets. Meaning of operations on sets There are many operations in maths like division, multiplication, addition, subtraction etc.When we apply these operations on numbers, we get a new number. Example: (a) If we multiply 4 by 5, we […]

Read More →

Rules of Addition and Subtraction of like Terms  In this lesson we will learn, how to add and subtract like terms Like Terms In an algebraic expression, like terms are terms that have same variables with same exponents and only the numerical coefficients of like terms are different. The terms must have the same variables […]

Read More →