Even Numbers: Definition, Example, Properties and List of Even Numbers from 1 to 1000 Definition: If we divide any integer by 2, and remainder is zero, we get an even number. Simply, If any integer divide exactly by 2, is an even number. The last digit of even numbers is 0, 2, 4, 6, 8. Example: 12, 10, […]
Read More →Parallel Intersecting and Perpendicular Lines Definition: Parallel Lines Two or more lines in a plane that never intersect or touch each other are called “Parallel lines”. The symbol “∥” is used to denote parallel lines. Example- PQ ∥ RS denoted that line PQ parallel to line RS. Intersecting lines […]
Read More →Disjoint Sets – Overlapping Sets Definition: Two are more sets are said to be ‘Disjoint sets’, if they have no common elements. or Disjoint sets are sets, whose Intersection is the empty set. Disjoint sets are also known as Non Overlapping sets. Let A and B are two […]
Read More →If a transversal intersects two lines, such that a pair of alternate interior angles are equal then the two lines are parallel. Given: Two lines AB and CD, and PS be transversal intersecting, AB at Q and CD at R. Each pair of alternate interior angles are equal. i.e. ∠BQR = ∠CRQ and ∠AQR = ∠QRD To Prove: AB ∥ CD Proof: Transversal […]
Read More →Equal chords of a circle subtend equal angles at the center. Given: Two equal chords AB and CD of a circle with center O. i,e. AB = CD. To prove: ∠AOB = ∠COD Proof: In △AOB and △ COD OA = OC (Radius of circle)OB = OD (Radius of circle)AB = CD (Given) Hence, △AOB ≅ △ COD (SSS Congruence rule) ∴ ∠AOB […]
Read More →A diagonal of a parallelogram, divides it into two congruent triangles. Given: A parallelogram ABCD and AC is a diagonal, the diagonal AC divides parallelogram ABCD into two triangles △ ABC and △ CDA. To prove: These triangles △ ABD and △CDA are congruent, △ ABC ≅ △ CDA Proof: In △ ABC and △ CDA BC ∥ AD and AC […]
Read More →In a parallelogram opposite sides are equal. Given: A parallelogram ABCD, each pair of Opposite sides of parallelogram are side AB and side DC and side AD and side BC. To prove: Opposite sides of parallelogram are equal that is AB = DC and AD = BC Construction: Join A to C that is AC, is a diagonal, the diagonal AC […]
Read More →If two Lines are parallel to a third line then the lines are parallel to each other. Given: It is given that three lines l, m, and n, and line l ∥ line m and line m ∥ line n. To Prove: Line l ∥ Line n Proof: Let us draw a line p transversal for lines l, m, and n. For lines l […]
Read More →Union of sets Definition: The Union of two sets A and B is the smallest set, which contains all the elements of both sets and taking every element of both sets A and B, without repeating any element, or common elements being taken only once. The symbol ‘∪’ used for the Union of two sets. Symbolically, we write union […]
Read More →Lowest Common Multiple Definition: The Lowest (smallest or least) common multiple, of two or more numbers, are called the “Lowest Common Multiple” (LCM). Example: Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30,……. and Example: Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, […]
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