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Newly added pages can be seen from this page. Keep visiting to this page so that you will remain updated.en-usMathWed, 11 Dec 2019 13:52:31 -0500Wed, 11 Dec 2019 13:52:31 -0500math-only-math.comDec 11, Worksheet on Factorization | Hints | Miscellaneous Factorization
https://www.math-only-math.com/Worksheet-on-Factorization.htmlf38c07077c6332e013dc81cbead2b5a5Practice the questions given in the Worksheet on Factorization. Factorization of expressions of the form a^3 ± b^3 1. Factorize: (i) 8x^3 + 27y^3 (ii) 216a^3 + 1 (iii) a^6 + 1 (iv) x^3 + \(\frac{1}{x^{3}}\) (v) a^3 + 8b^6Wed, 11 Dec 2019 13:52:29 -0500Dec 9, Factorization of expressions of the Form a^3 + b^3 + c^3 – 3abc
https://www.math-only-math.com/factorization-of--expressions-of-the-form-a-cube-plus-b-cube-plus-c-cube-minus-3abc.html90cf66f59a98dffa1d646ece2b2afbedHere we will learn the process of On Factorizations of expressions of the Form a^3 + b^3 + c^3 – 3abc. We have, a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 – bc – ca – ab). [Verify by actual multiplication.] Example: Factorize: x^3 + y^3 – 3xy + 1. Solution: HereMon, 9 Dec 2019 13:00:28 -0500Dec 9, Factorization of Expressions of the Form a^3 + b^3 + c^3, a + b + c=0
https://www.math-only-math.com/factorization-of-expressions-of-the-form-a-cube-plus-b-cube-plus-c-cube.html127b37b29670a1231cbeed6f8edf6be3Here we will learn the process of On Factorization of expressions of the Form a^3 + b^3 + c^3 , where a + b + c = 0. We have, a^3 + b^3 + c^3 = a^3 + b^3 – (-c)^3 = a^3 + b^3 – (a + b)^3, [Since, a + b + c = 0] = a^3 + b^3 – {a^3 + b^3 + 3ab(a + b)} = -3ab(a + b) = -3ab(-cMon, 9 Dec 2019 12:49:59 -0500Dec 9, Miscellaneous Problems on Factorization | Application Problems
https://www.math-only-math.com/miscellaneous-problems-on-factorization.html54cffd60de675f72071defa110bcab76Here we will solve different types of Miscellaneous Problems on Factorization. 1. Factorize: x(2x + 5) – 3 Solution: Given expression = x(2x + 5) – 3 = 2x^2 + 5x – 3 = 2x^2 + 6x – x – 3, [Since, 2(-3) = - 6 = 6 × (-1), and 6 + (-1) = 5] = 2x(x + 3) – 1(x + 3)Mon, 9 Dec 2019 12:38:53 -0500Nov 24, Factorization of Expressions of the Form a^3 - b^3 | Solved Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-a-cube-minus-b-cube.html0fb19ef636a9c0a28b9d0e5dcb4be177Here we will learn the process of Factorization of Expressions of the Form a^3 - b^3. We know that (a - b)^3 = a^3 - b^3 - 3ab(a - b), and so a^3 - b^3 = (a - b)^3 + 3ab(a - b) = (a - b){(a - b)^2 + 3ab} Therefore, a^3 - b^3 = (a - b)(a^2 + ab + b^2) Example: 1. Factorize:Sun, 24 Nov 2019 11:06:29 -0500Nov 24, Factorization of Expressions of the Form a^3 + b^3 | Solved Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-a-cube-plus-b-cube.htmla42ffad5bcf2c556c67a3177acd9a85aHere we will learn the process of Factorization of Expressions of the Form a^3 + b^3. We know that (a + b)^3 = a^3 + b^3 + 3ab(a + b), and so a^3 + b^3 = (a + b)^3 – 3ab(a + b) = (a + b){(a + b)^2 – 3ab} Therefore, a^3 + b^3 = (a + b)(a^2 – ab + b^2). Example: 1. Factorize:Sun, 24 Nov 2019 10:52:36 -0500Nov 23, Worksheet on Factorization of the Trinomial ax^2 + bx + c | Answers
https://www.math-only-math.com/worksheet-on-factorization-of-the-trinomial-ax-square-plus-bx-plus-c.html1b16a9412ab882790032cd86fbbc52f4Practice the questions given in the worksheet on factorization of the trinomial ax^2 + bx + c. 1. Factorization of a perfect-square trinomial. (i) a^2 + 6a + 9 (ii) a^2 + a + \(\frac{1}{4}\) (iii) 25x^2 – 10x + 1 (iv) 4x^2 – 4xy + y^2 2. Factorization of expressions of theSat, 23 Nov 2019 14:31:18 -0500Nov 18, Problems on Factorization of Expressions of the Form x^2 +(a + b)x +ab
https://www.math-only-math.com/problems-on-factorization-of-expressions-of-the-form-ax-square-plus-bx-plus-c.html52ef5c4880c0d3668031380c8abe9ac4Here we will solve different types of Problems on Factorization of Expressions of the Form x^2 + (a + b)x + ab. 1. Factorize: a^2 + 25a - 54 Solution: Here, constant term = -54 = (27) × (-2), and 27 + (-2) = 25 (= coefficient of a). Therefore, a^2 + 25a – 54Mon, 18 Nov 2019 13:51:37 -0500Nov 17, Factorization of Expressions of the Form ax^2 + bx + c, a ≠ 1|Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-ax-square-plus-bx-plus-c.htmlf223af9f9b881f4d62425eb511376a4aThe below examples show that the method of factorizing ax^2 + bx + c by breaking the middle term involves the following steps. Steps: 1.Take the product of the constant term and the coefficient of x^2, i.e., ac. 2. Break ac into two factors p, q whose sum is b,Sun, 17 Nov 2019 13:49:20 -0500Nov 13, Factorization of Expressions of the Form x^2 + (a + b)x + ab |Examples
https://www.math-only-math.com/factorization-of-expressions-of-the-form-x-square-plus-sum-of-a-plus-b-times-x-plus-a-times-b.html14b60cc9e9671950d97dd82aa69a460aHere we will learn the process of Factorization of Expressions of the Form x^2 + (a + b)x + ab. We know, (x + a)(x + b) = x^2 + (a + b)x + ab. Therefore, x^2 + (a + b)x + ab = (x + a)(x + b). 1. Factorize: a^2 + 7a + 12. Solution: Here, constant term = 12 = 3 × 4, and 3 + 4Wed, 13 Nov 2019 09:52:29 -0500Nov 10, Factorization of a Perfect-square Trinomial | Solved Examples
https://www.math-only-math.com/factorization-of-a-perfect-square-trinomial.html48890bf9ac661b367380b99213c79577Here we will learn the process of Factorization of a Perfect-square Trinomial. A trinomial of the form a^2 ± 2ab + b^2 = (a ± b)^2 = (a ± b)(a ± b) Solved examples on Factorization of a Perfect-square Trinomial 1. Factorize: x^2 + 6x + 9 Solution: Here, given expressionSun, 10 Nov 2019 13:12:44 -0500Nov 4, Problems on Factorization Using a^2 – b^2 = (a + b)(a – b)
https://www.math-only-math.com/problems-on-factorization-using-a-square-minus-b-square.html8a59984ada7331124d57659e85003826Problems on Factorization using a^2 – b^2 = (a + b)(a – b) Here we will solve different types of Problems on Factorization using a^2 – b^2 = (a + b)(a – b). 1. Factorize: 4a^2 – b^2 + 2a + b Solution: Given expression = 4a^2 – b^2 + 2a + b = (4a^2 – b^2) + 2a + bMon, 4 Nov 2019 14:04:42 -0500Nov 2, Problems on Factorization of Expressions of the Form a^2 – b^2
https://www.math-only-math.com/problems-on-factorization-of-expressions-of-the-form-a-square-minus-b-square.html1da0069d0fa9ba719bd72fca8ebce9a4Here we will solve different types of Problems on Factorization of expressions of the form a^2 – b^2. 1. Resolve into factors: 49a^2 – 81b^2 Solution: Given expression = 49a^2 – 81b^2 = (7a)^2 – (9b)^2 = (7a + 9b)(7a – 9b). 2.Factorize: (x + y)^2 – 4(x - y)^2 Solution: GivenSat, 2 Nov 2019 15:17:28 -0400Nov 1, Problems on Factorization by Grouping of Terms | Find the Factors
https://www.math-only-math.com/problems-on-factorization-by-grouping-of-terms.html58b0925cbd73933595bfd525bb311482Here we will solve different types of Problems on Factorization by grouping of terms. 1. Factorize: a^2 – (b – 5)a – 5b. Solution: Given expression = a^2 – (b – 5)a – 5b = a^2 – ba + 5a – 5b = a(a - b) + 5(a - b) = (a – b)(a + 5). 2. Factorize: a^2 + b^2 + a + b + 2abFri, 1 Nov 2019 14:53:22 -0400Oct 31, Introduction to Factorization | Different of Two Squares | Examples
https://www.math-only-math.com/introduction-to-factorization.html36e9e8be9928b1fa1c56e66a1672d53bWe will discuss here about the introduction to factorization. The method of expressing a given polynomial as a product of two or more polynomials is called factorization. The polynomials whose product is the given polynomial are called its factors. You are already familiarThu, 31 Oct 2019 14:09:58 -0400Oct 25, Problems on Expanding of (a ± b)\(^{3}\) and its Corollaries |Examples
https://www.math-only-math.com/problems-on-expansion-of-a-plus-minus-b-whole-cube-and-its-corollaries.html7a82e6578ca9cb4da42f220edf5f5110Here we will solve different types of application problems on expanding of (a ± b)\(^{3}\) and its corollaries. 1. Expanding the following: (i) (1 + x)\(^{3}\) (ii) (2a – 3b)\(^{3}\) (iii) (x + \(\frac{1}{x}\))\(^{3}\) Solution: (i) (1 + x)\(^{3}\) = 1\(^{3}\) +Fri, 25 Oct 2019 18:02:47 -0400Oct 22, Worksheet on Application Problems on Expansion of Powers of Binomials
https://www.math-only-math.com/worksheet-on-application-problems-on-expansion-of-powers-of-binomials-and-trinomials.html21d7f54c3e6359bc86902df6d709caa2Practice the questions given in the worksheet on application problems on expansion of powers of binomials and trinomials. 1. Use (a ± b)^2 = a^2 ± 2ab + b2 to evaluate the following: (i) (3.001)^2 (ii) (5.99)^2 (iii) 1001 × 999 (iv) 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37Tue, 22 Oct 2019 11:38:36 -0400Oct 22, Application Problems on Expansion of Powers of Binomials & Trinomials
https://www.math-only-math.com/application-problems-on-expansion-of-powers-of-binomials-and-trinomials.htmlde09bec634791c1c307f991f118e9eaaHere we will solve different types of application problems on expansion of powers of binomials and trinomials. 1. Use (x ± y)^2 = x^2 ± 2xy + y^2 to evaluate (2.05)^2. Solution: (2.05)^2 = (2 + 0.05)^2 = 2^2 + 2 × 2 × 0.05 + (0.05)^2 = 4 + 0.20 + 0.0025 = 4.2025.Tue, 22 Oct 2019 11:30:44 -0400Oct 21, Expansion of (x + a)(x + b)(x + c) | Solved Examples | Problems | Hint
https://www.math-only-math.com/expansion-of-x-plus-a-times-x-plus-b-times-x-plus-c.html72f2294e1523dd5870b712a506e4fda8We will discuss here about the expansion of (x + a)(x + b)(x + c). (x + a)(x + b)(x + c) = (x + a){(x + b)(x + c)} = (x + a){x\(^{2}\) + (b + c)x + bc} = x{x\(^{2}\) + (b + c)x + bc} + a{x\(^{2}\) + (b + c)x + bc} = x\(^{3}\) + (b + c)x\(^{2}\) + bcx + ax\(^{2}\) + a(b + c)xMon, 21 Oct 2019 13:13:08 -0400Oct 20, Simplification of (a + b + c)(a\(^{2}\)+b\(^{2}\)+c\(^{2}\)–ab–bc– ca)
https://www.math-only-math.com/simplification-of-a-cube-plus-b-cube-plus-c-cube-minus-three-abc.html2b68a2ce4c6e5f303265f70c1721d2bcWe will discuss here about the expansion of (a + b + c)(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – ab – bc – ca). (a + b + c)(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – ab – bc – ca) = a(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) – ab – bc – ca) + b(a\(^{2}\) + b\(^{2}\) + c\(^{2}\) –ab – bc – ca)Sun, 20 Oct 2019 11:37:12 -0400Oct 17, Simplification of (a ± b)(a^2 ∓ ab + b^2) | Sum or Difference of Cubes
https://www.math-only-math.com/simplification-of-a-cube-plus-minus-b-cube.html525b25cc2dc1d18243ccbb623e59a90fWe will discuss here about the expansion of (a ± b)(a\(^{2}\) ∓ ab + b\(^{2}\)). (a + b)(a\(^{2}\) - ab + b\(^{2}\)) = a(a\(^{2}\) - ab + b\(^{2}\)) + b(a\(^{2}\) - ab + b\(^{2}\)) = a\(^{3}\) - a\(^{2}\)b + ab\(^{2}\) + ba\(^{2}\) - ab\(^{2}\) + b\(^{3}\) =Thu, 17 Oct 2019 12:17:46 -0400Oct 15, Expansion of (a ± b)\(^{3}\) | Algebraic Expressions and Formulas
https://www.math-only-math.com/expansion-of-a-plus-minus-b-whole-cube.html50dd2e004723f6e82f18b50203e5ee4fWe will discuss here about the expansion of (a ± b)\(^{3}\). (a + b)\(^{3}\) = (a + b) ∙ (a + b)\(^{2}\) = (a + b)(a\(^{2}\) + 2ab + b\(^{2}\)) = a(a\(^{2}\) + 2ab + b\(^{2}\)) + b(a\(^{2}\) + 2ab + b\(^{2}\))=a\(^{3}\)+2a\(^{2}\)b+ab\(^{2}\)+ba\(^{2}\)+2ab\(^{2}\)+b\(^{3}\)Tue, 15 Oct 2019 11:49:46 -0400Oct 14, Express a^2 + b^2 + c^2 – ab – bc – ca as Sum of Squares
https://www.math-only-math.com/express-as-sum-of-squares.html1f589af3cf1952bdc53ae88223b19e67Here we will express a^2 + b^2 + c^2 – ab – bc – ca as sum of squares. If a, b, c are real numbers then (a – b)^2, (b – c)^2 and (c – a)^2 are positive as square of every real number is positive. So, a^2 + b^2 + c^2 – ab – bc – ca is always positive.Mon, 14 Oct 2019 14:07:43 -0400Oct 11, Worksheet on Simplification of (a + b)(a – b) | Hint | Answers
https://www.math-only-math.com/worksheet-on-simplification-of-the-product-of-a-plus-b-and-a-minus-b.html4201253dd23654fab680fb63accf0d25Practice the questions given in the worksheet on simplification of (a + b)(a – b). 1. Simplify by applying standard formula. (i) (5x – 9)(5x + 9) (ii) (2x + 3y)(2x – 3y) (iii) (a + b – c)(a – b + c) (iv) (x + y – 3)(x + y + 3) (v) (1 + a)(1 – a)(1 + a^2)Fri, 11 Oct 2019 17:17:00 -0400Oct 10, Worksheet on Completing Square |Find the Missing Term| Perfect Squares
https://www.math-only-math.com/worksheet-on-completing-a-square.html388ee09538142e6b0d041bf825e94462Practice the questions given in the worksheet on completing square. Write the following as a perfect square. (i) 4X^2 + 4X + 1 (ii) 9a^2 – 12ab + 4b^2 (iii) 1 + 6/a + 9/a^2 2. Indicate the perfect squares among the following. Express each of the perfect squares as the squareThu, 10 Oct 2019 12:56:07 -0400Oct 10, Completing a Square | Solved Examples on Completing a Square
https://www.math-only-math.com/completing-a-square.htmlc2d566000272f00680a11a39f5ccae3bHere we will learn how to completing a square.Problems on completing a square 1. What should be added to the polynomial 4m^2 + 8m so that it becomes perfect square? Solution: 4m^2 + 8m = (2m)^2 + 2 ∙ (2m) ∙ 2Thu, 10 Oct 2019 12:22:16 -0400Oct 9, Worksheet on Expansion of (x ± a)(x ± b) | Find the Product | Answers
https://www.math-only-math.com/worksheet-on-expansion-of-the-product-of-x-plus-minus-a-and-x-plus-minus-b.html00349c09970702c3a5245b092cbb2f21Practice the questions given in the worksheet on expansion of (x ± a)(x ± b). 1. (i) Find the product using standard formula. (i) (x + 2)(x + 5) (ii) (a – 4)(a – 7) (iii) (x + 1)(x – 8) (iv) (a – 3)(a + 2) (v) (3x + 1)(3x + 2) (vi) (4x – y)(4x + 2y) 2. Find the product.Wed, 9 Oct 2019 15:32:17 -0400Oct 1, Worksheet on Expanding of (a ± b ± c)^2 and its Corollaries | Answers
https://www.math-only-math.com/worksheet-on-expansion-of-a-plus-minus-b-plus-minus-c-whole-square-and-its-corollaries.html10839011dd64723ae2a3fac3d32c54b8Practice the questions given in the worksheet on expanding of (a ± b ± c)^2 and its corollaries. 1. Expand the squares of the following trinomials. (i) a + 2b + 3c (ii) 2x + 3y + 4z (iii) x + 2y – 3z (iv) 3a – 4b – c (v) 1 – x - \(\frac{1}{x}\) (vi) 1 – a – a^2. 2. Simplify:Tue, 1 Oct 2019 11:24:15 -0400Sep 30, Worksheet on Expansion of (a ± b)^2 and its Corollaries | Answers
https://www.math-only-math.com/worksheet-on-expansion-of-a-plus-minus-b-whole-square-and-its-corollaries.htmla63c032991f36d3f971d8cae44cefff8Practice the questions given in the worksheet on expansion of (a ± b)^2 and its corollaries. 1. Expand the squares of the following: (i) 4x + y (ii) 5a + 3b (iii) 2x + \(\frac{1}{x}\) 2. Expand the following: (i) (x – 2y)^2 (ii) (3y – 2z)^2 (iii) (3x - \(\frac{1}{3x}\))^2Mon, 30 Sep 2019 18:40:36 -0400Sep 23, Simplification of (a + b)(a – b) | | Solved Examples on Simplification
https://www.math-only-math.com/simplification-of-the-product-of-a-plus-b-and-a-minus-b.html4107bee1e909ea2b94f6bff45837090fWe will discuss here about the Simplification of (a + b)(a – b). (a + b)(a – b) = a(a – b) + b(a – b) = a\(^{2}\) - ab + ba - b\(^{2}\) = a\(^{2}\) - b\(^{2}\) Thus, we have (a + b)(a - b) = a\(^{2}\) - b\(^{2}\) Solved Examples on Simplification of (a + b)(a – b) 1.Mon, 23 Sep 2019 10:19:44 -0400Sep 22, Expansion of (x ± a)(x ± b) | Special Identities | Expanding Binomials
https://www.math-only-math.com/expansion-of-the-product-of-x-plus-minus-a-and-x-plus-minus-b.htmlf35606e89057f8ca4efdf559232b995eWe will discuss here about the expansion of (x ± a)(x ± b) (x + a)(x + b) = x(x + b) + a (x + b) = x^2 + xb + ax + ab = x^2 + (b + a)x + ab (x - a)(x - b) = x(x - b) - a (x - b) = x^2 - xb - ax + ab = x^2 - (b + a)x + ab (x + a)(x - b) = x(x - b) + a (x - b) = x^2 - xb Sun, 22 Sep 2019 13:58:25 -0400Sep 22, Expansion of (a ± b ± c)^2 | Square of a Trinomial | Algebra Formulas
https://www.math-only-math.com/expansion-of-a-plus-minus-b-plus-minus-c-whole-square.html08c7c163459f15be3f817c2fb0d96ed0We will discuss here about the expansion of (a ± b ± c)^2. (a + b + c)^2 = {a + (b + c)}^2 = a^2 + 2a(b + c) + (b + c)^2 = a^2 + 2ab + 2ac + b^2 + 2bc + c^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) = sum of squares of a, b, c + 2(sum of the products of a, b, c taking two at a tiSun, 22 Sep 2019 11:02:52 -0400Sep 21, A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles
https://www.math-only-math.com/a-rhombus-is-a-parallelogram-whose-diagonals-meet-at-right-angles.htmle62cfb3b5b2d921b3380bbd941894ca6Here we will prove that a rhombus is a parallelogram whose diagonals meet at right angles. Given: PQRS is a rhombus. So, by definition, PQ = QR = RD = SP. Its diagonals PR and QS intersect at O. To prove: (i) PQRS is a parallelogram. (ii) ∠POQ = ∠QOR = ∠ROS = ∠SOP = 90°.Sat, 21 Sep 2019 17:34:35 -0400Sep 21, Pair of Opposite Sides of a Parallelogram are Equal and Parallel
https://www.math-only-math.com/pair-of-opposite-sides-of-a-parallelogram-are-equal-and-parallel.html8f16ce62bfe73e65784fa3a855a68d5bHere we will discuss about one of the important geometrical property of parallelogram. A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel Given: PQRS is a quadrilateral in which PQ = SR and PQ ∥ SR. To prove: PQRS is a parallelogram.Sat, 21 Sep 2019 17:20:41 -0400Sep 21, A Quadrilateral is a Parallelogram if its Diagonals Bisect each Other
https://www.math-only-math.com/a-quadrilateral-is-a-parallelogram-if-its-diagonals-bisect-each-other.html135e7b7c04ff496035756b1d3770af54Here we will discuss about a quadrilateral is a parallelogram if its diagonals bisect each other. Given: PQRS is a quadrilateral whose diagonals PR and QS bisect each other at O, i.e., OP = OR and OQ = OS. To prove: PQRS is a parallelogram. Proof: In ∆OPQ and ∆ORS, OP = ORSat, 21 Sep 2019 16:49:01 -0400Sep 21, Diagonals of a Parallelogram Bisect each Other | Diagonals Bisect each
https://www.math-only-math.com/diagonals-of-a-parallelogram-bisect-each-other.html9cbbc2ced76b29141b62d992d0005cd9Here we will discuss about the diagonals of a parallelogram bisect each other. In a parallelogram, diagonals bisect each other and each diagonal bisects the parallelogram into two congruent triangles. Given: PQRS is a parallelogram in which PQ ∥ SR and PS ∥ QR. Its diagonalsSat, 21 Sep 2019 15:27:35 -0400Sep 20, Expansion of (a ± b)^2 | Power of the Trinomial | Algebraic Expression
https://www.math-only-math.com/expansion-of-a-plus-minus-b-whole-square.html37ca8e866688946927f0b48a9f8ee399A binomial is an algebraic expression which has exactly two terms, for example, a ± b. Its power is indicated by a superscript. For example, (a ± b)2 is a power of the binomial a ± b, the index being 2. A trinomial is an algebraic expression which has exactly three termsFri, 20 Sep 2019 18:47:33 -0400Sep 18, Opposite Angles of a Parallelogram are Equal | Related Solved Examples
https://www.math-only-math.com/opposite-angles-of-a-parallelogram-are-equal.htmld514b8b7a64661180d3d25c39285acb0Here we will discuss about the opposite angles of a parallelogram are equal. In a parallelogram, each pair of opposite angles are equal. Given: PQRS is a parallelogram in which PQ ∥ SR and QR ∥ PS To prove: ∠P = ∠R and ∠Q = ∠S Construction: Join PR and QS. Proof: Statement:Wed, 18 Sep 2019 18:16:50 -0400Sep 18, Opposite Sides of a Parallelogram are Equal | Solved Examples
https://www.math-only-math.com/opposite-sides-of-a-parallelogram-are-equal.html677aa4b6b32c8665a0f3fefd9b42a7cdHere we will discuss about the opposite sides of a parallelogram are equal in length. In a parallelogram, each pair of opposite sides are of equal length. Given: PQRS is a parallelogram in which PQ ∥ SR and QR ∥ PS. To prove: PQ = SR and PS = QR. Construction: Join PRWed, 18 Sep 2019 17:30:25 -0400Sep 17, Concept of Parallelogram |Quadrilateral| Rectangle| Rhombus| Trapezium
https://www.math-only-math.com/concept-of-parallelogram.html4cc41004c4cec39e072024140d4c5735Here we will discuss about the concept of parallelogram. Quadrilateral: A rectilinear figure enclosed by four line segments is called a quadrilateral. In the adjoining figures, we have two quadrilaterals PQRS, each enclosed by four line segments PQ, QR, RS and SP whichTue, 17 Sep 2019 18:00:01 -0400Sep 5, Diagonal of a Quadrilateral Divides it in Two Triangles of Equal Area
https://www.math-only-math.com/diagonal-of-a-quadrilateral-divides-it-in-two-triangles-of-equal-area.html08a86273ff27b19cafa8bcce86ea7925Here we will prove that if each diagonal of a quadrilateral divides it in two triangles of equal area then prove that the quadrilateral is a parallelogram. Solution: Given: PQRS is a quadrilateral whose diagonals PR and QS cut at O such that ar(∆PQR) = ar(∆PSR), andThu, 5 Sep 2019 18:12:32 -0400Aug 26, The Area of a Rhombus is Equal to Half the Product of its Diagonals
https://www.math-only-math.com/the-area-of-a-rhombus-is-equal-to-half-the-product-of-its-diagonals.html4962fd2984646b1c654631035f21c8c7Here we will prove that the area of a rhombus is equal to half the product of its diagonals. Solution: Given: PQRS is a rhombus whose diagonals are PR and QS. The diagonals intersect at O. To prove: ar(rhombus PQRS) = 1/2 ×PR × QS. Statement ar(∆RSQ) = 1/2 ×Base × AltitudeMon, 26 Aug 2019 15:32:28 -0400Aug 25, Area of the Triangle formed by Joining the Middle Points of the Sides
https://www.math-only-math.com/area-of-the-triangle-formed-by-joining-the-middle-points-of-the-sides-of-a-triangle.html2c54f6b8b7ac91f59a369648af098ce2Here we will prove that the area of the triangle formed by joining the middle points of the sides of a triangle is equal to one-fourth area of the given triangle. Solution: Given: X, Y and Z are the middle points of sides QR, RP and PQ respectively of the triangle PQR.Sun, 25 Aug 2019 16:53:47 -0400Aug 22, Problems on Finding Area of Triangle and Parallelogram | With Diagram
https://www.math-only-math.com/problems-on-finding-area-of-triangle-and-parallelogram.html56979c378cc6c4bae48a4122af303ac5Here we will learn how to solve different types of problems on finding area of triangle and parallelogram. 1. In the figure, XQ ∥ SY, PS ∥ QR, XS ⊥ SY, QY ⊥ SY and QY = 3 cm. Find the areas of ∆MSR and parallelogram PQRS. Solution: ar(∆MSR) = 1/2 × ar(rectangle of SRThu, 22 Aug 2019 17:04:59 -0400Aug 19, Triangles with Equal Areas on the Same Base have Equal Corresponding..
https://www.math-only-math.com/triangles-with-equal-areas-on-the-same-base-have-equal-corresponding-altitudes.html1c9c6694e77dcb0dd0365e6d76db55a3Here we will prove that triangles with equal areas on the same base have equal corresponding altitudes (or are between the same parallels). Given: PQR and SQR are two triangles on the same base QR, and ar(∆PQR) = ar(∆SQC). Also, PN and SM are their corresponding altitudes.Mon, 19 Aug 2019 16:41:20 -0400Aug 18, Triangles on the Same Base & between Same Parallels are Equal in Area
https://www.math-only-math.com/triangles-on-the-same-base-and-between-the-same-parallels-are-equal-in-area.html3d65fece0d51ab8dad34dcc5dfc300d8Here we will prove that triangles on the same base and between the same parallels are equal in area. Given: PQR and SQR are two triangles on the same base QR and are between the same parallel lines QR and MN, i.e., P and S are on MN. To prove: ar(∆PQR) = ar(∆SQR)Sun, 18 Aug 2019 16:19:21 -0400Aug 17, Area of a Triangle is Half that of a Parallelogram on the Same Base
https://www.math-only-math.com/area-of-a-triangle-is-half-that-of-a-parallelogram-on-the-same-base-and-between-the-same-parallels.html52671967f84c9a51ae2645ad5fc4d4caHere we will prove that the area of a triangle is half that of a parallelogram on the same base and between the same parallels. Given: PQRS is a parallelogram and PQM is a triangle with the same base PQ, and are between the same parallel lines PQ and SR.Sat, 17 Aug 2019 17:00:18 -0400Aug 14, Area of a Parallelogram is Equal to that of a Rectangle Between ......
https://www.math-only-math.com/area-of-a-parallelogram-is-equal-to-that-of-a-rectangle-between-the-same-parallel-lines.html5e86da61c46e3782249c83dd30dd8a3bHere we will prove that the area of a parallelogram is equal to that of a rectangle on the same base and of the same altitude, that is between the same parallel lines. Given: PQRS is a parallelogram and PQ MN is a rectangle on the same base PQ and between the same parallelWed, 14 Aug 2019 11:55:57 -0400Aug 13, Parallelogram on the Same Base and Between the Same Parallel Lines
https://www.math-only-math.com/parallelogram-on-the-same-base-and-between-the-same-parallel-lines-are-equal-in-area.htmla0e7fe8fd3f951c8d348f7e7ee27b7faHere we will prove that parallelogram on the same base and between the same parallel lines are equal in area. Given: PQRS and PQMN are two parallelograms on the same base PQ and between same parallel lines PQ and SM. To prove: ar(parallelogram PQRS) = ar(parallelogram PQMN).Tue, 13 Aug 2019 16:17:25 -0400Aug 11, Diagonal of a Parallelogram Divides it into Two Triangles of EqualArea
https://www.math-only-math.com/every-diagonal-of-a-parallelogram-divides-it-into-two-triangles-of-equal-area.htmlccccf7e508789cf471850bacd7c4d37eHere we will prove that every diagonal of a parallelogram divides it into two triangles of equal area. Given: PQRS is a parallelogram in which PQ ∥ SR and SP ∥ RQ. PR is a diagonal of the parallelogram. To prove: ar(∆PSR) = ar(∆RQP). Proof: Statement 1. ∠SPR = ∠PRQ. 2. ∠SRPSun, 11 Aug 2019 13:10:55 -0400Aug 11, Base and Height (Altitude) in a Triangle and a Parallelogram | Diagram
https://www.math-only-math.com/base-and-height-in-a-triangle-and-a-parallelogram.html7a3a8459165d946b4d253db00f289233We will discuss here about the Base and height (altitude) in a triangle and a parallelogram. In ∆PQR, any side may be taken as the base. If QR is taken as the base then the perpendicular PM on QR is the corresponding altitude (height) of the triangle. In the parallelogramSun, 11 Aug 2019 12:07:03 -0400Aug 8, Area of a Closed Figure |Measurement of Area |Area Axiom for Rectangle
https://www.math-only-math.com/area-of-a-closed-figure.html1d41e2a516c37581287f6e2181890794We will discuss here about the area of a closed figure, measurement of area, area axiom for rectangle, area axiom for congruent figures and addition axiom for area. The measure of the reason bounded by a closed figure in a plane is called its area. In the following the areasThu, 8 Aug 2019 17:43:18 -0400Aug 6, Bisectors of the Angles of a Parallelogram form a Rectangle | Diagram
https://www.math-only-math.com/bisectors-of-the-angles-of-a-parallelogram-form-a-rectangle.htmle157bbf5124d9fbd72f7a7de5b17bab8Here we will prove that the bisectors of the angles of a parallelogram form a rectangle. Given: PQRS is a parallelogram in which PQ ∥ SR and SP ∥ RQ. The bisectors of ∠P, ∠Q, ∠R and ∠S are PJ, QK, RL and SM respectively which enclose the quadrilateral JKLM. To prove: JKLM isTue, 6 Aug 2019 16:18:18 -0400Aug 2, Conditions for Classification of Quadrilaterals and Parallelograms
https://www.math-only-math.com/classification-of-quadrilaterals-and-parallelograms.htmlc41587777493d51d3fff2e256895f446We will discuss here about Conditions for classification of quadrilaterals and parallelograms. On the basis of the above definitions, theorems and converse propositions we conclude the following. 1. A quadrilateral is a parallelogram if any one of the following holds.Fri, 2 Aug 2019 15:29:34 -0400Aug 1, Diagonals of a Parallelogram are Equal & Intersect at Right Angles
https://www.math-only-math.com/parallelogram-will-be-a-square.htmlc239f7bc1a75321cc40db5e6f92725d8Here we will prove that if in a parallelogram the diagonals are equal in length and intersect at right angles, the parallelogram will be a square. Given: PQRS is a parallelogram in which PQ ∥ SR, PS ∥ QR and diagonal PR ⊥diagonal QS. To prove: PQRS is a square, i.e., PQThu, 1 Aug 2019 16:50:40 -0400Aug 1, Diagonals of a Square are Equal in Length & they Meet at Right Angles
https://www.math-only-math.com/diagonals-of-a-square-are-equal-in-length-and-they-meet-at-right-angles.html999cc80626505b351b6b2c70c15e94a2Here we will prove that in a square, the diagonals are equal in length and they meet at right angles. Given: PQRS is a square in which PQ = QR = RS = SP, and ∠QPS = ∠PQR = ∠QRS = ∠RSP = 90°. To prove: PR = QS and PR ⊥ QS Proof: Statement 1. In ∆SPQ and ∆RQP, (i) SP = QRThu, 1 Aug 2019 11:10:59 -0400Jul 29, A Parallelogram, whose Diagonals are of Equal Length, is a Rectangle
https://www.math-only-math.com/a-parallelogram-whose-diagonals-are-of-equal-length-is-a-rectangle.htmlb1f04147ae9b244d05694d39f27a1941Here we will prove that a parallelogram, whose diagonals are of equal length, is a rectangle. Given: PQRS is a parallelogram in which PQ ∥ SR, PS ∥ QR and PR = QS. To prove: PQRS is a parallelogram, i.e., in the parallelogram PQRS, one angle, say ∠QPS = 90°. Proof: In ∆PQRMon, 29 Jul 2019 16:42:35 -0400Jul 25, In a Rectangle the Diagonals are of Equal Lengths | Proof | Diagram
https://www.math-only-math.com/in-a-rectangle-the-diagonals-are-of-equal-lengths.html5383babc1985e7d26a6aa4b5eeb2b7f9Here we will prove that in a rectangle the diagonals are of equal lengths. Given: PQRS is rectangle in which PQ ∥ SR, PS ∥ QR and ∠PQR = ∠QRP = ∠RSP = ∠SPQ = 90°. To prove: The diagonals PR and QS are equal. Proof: Statement In ∆PQR and ∆RSP 1.∠QPR = ∠SRP 2. ∠QRP = ∠SPRThu, 25 Jul 2019 15:45:55 -0400Jul 25, A Parallelogram whose Diagonals Intersect at Right Angles is a Rhombus
https://www.math-only-math.com/a-parallelogram-whose-diagonals-intersect-at-right-angles-is-a-rhombus.html16f5ddd6d104751b1f5b5da51c17c1ccHere we will prove that a parallelogram, whose diagonals intersect at right angles, is a rhombus. Given: PQRS is a parallelogram in which PQ ∥ SR, PS ∥ QR and ∠QOR = ∠POQ = ∠ROS = ∠POS = 90°. To prove: PQRS is a rhombus, i.e., PQ = QR = RS = SP. Proof: In ∆PQR and ∆RSP,Thu, 25 Jul 2019 15:07:54 -0400