{"id":67271,"date":"2023-08-30T18:38:00","date_gmt":"2023-08-30T13:08:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=67271"},"modified":"2023-12-15T15:47:09","modified_gmt":"2023-12-15T10:17:09","slug":"rs-aggarwal-chapter-7-class-9-maths-exercise-7-1-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-7-class-9-maths-exercise-7-1-solutions\/","title":{"rendered":"RS Aggarwal Chapter 7 Class 9 Maths Exercises 7.1 (ex 7a) Solutions"},"content":{"rendered":"\n<p>RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions: You have also studied some axioms and, with the help of these axioms, you proved some other statements. In this chapter, you will study the properties of the angles formed when two lines intersect each other, and also the properties of the angles formed when a line intersects two or more parallel lines at distinct points. Further, you will use these properties to prove some statements using deductive reasoning. You have already verified these statements through some activities in the earlier classes. Know more on <a href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-solutions-class-9-maths-chapter-7-lines-and-angles\/\">Line and Angles here<\/a>.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69da538047c08\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69da538047c08\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-7-class-9-maths-exercise-7-1-solutions\/#download-rs-aggarwal-chapter-7-class-9-maths-exercise-71-solutions\" title=\"Download RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions\">Download RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-7-class-9-maths-exercise-7-1-solutions\/#important-definition-for-rs-aggarwal-chapter-7-class-9-maths-ex-7a-solutions\" title=\"Important Definition for RS Aggarwal Chapter 7\u00a0Class 9\u00a0Maths Ex 7a\u00a0Solutions\">Important Definition for RS Aggarwal Chapter 7\u00a0Class 9\u00a0Maths Ex 7a\u00a0Solutions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rs-aggarwal-chapter-7-class-9-maths-exercise-71-solutions\"><\/span>Download RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/EXERCISE-7A.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/EXERCISE-7A.pdf\">EXERCISE 7A<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definition-for-rs-aggarwal-chapter-7-class-9-maths-ex-7a-solutions\"><\/span>Important Definition for RS Aggarwal Chapter 7\u00a0Class 9\u00a0Maths Ex 7a\u00a0Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions<\/p>\n<p>Point: A point is a dot made by a sharp pen or pencil. It is represented by capital letters.<\/p>\n<p>Line: A straight and endless path on both directions is called a line.<\/p>\n<p>Line segment: A line segment is a straight path between two points.<\/p>\n<p>Ray: A ray is a straight path that goes forever in one direction.<\/p>\n<p>Collinear points: If three or more than three points lie on the same line, then they are called collinear points.<\/p>\n<p>Non-collinear points: If three or more than three points do not lie on the same line, then they are called non-collinear points.<\/p>\n<p>Angle: The space between two straight lines that diverge from a common point or between two planes that extend from a common line.<br \/>Types of Angles<br \/>1. Acute angle: An angle between 0\u00b0 and 90\u00b0 is called acute angle.<\/p>\n<ol start=\"2\">\n<li>Right angle: An angle that is equal to 90\u00b0 is called a right angle.<\/li>\n<li>Obtuse angle: An angle which is more than 90\u00b0 but less than 180\u00b0 is called obtuse angle.<\/li>\n<li>Straight angle: An angle whose measure is 180\u00b0 is called a straight angle.<\/li>\n<li>Reflex angle: An angle whose measure is between 180\u00b0 and 360\u00b0 is called reflex angle.<\/li>\n<li>Complete angle: An angle which is equal to 360\u00b0 is called complete angle<\/li>\n<\/ol>\n<p>RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions: Pairs of Angles<\/p>\n<p>1. Complementary angles: Two angles are said to be complementary if the sum of their degree measure is 90\u00b0.<\/p>\n<p>For example, a pair of complementary angles are 35\u00b0 and 55\u00b0.<\/p>\n<ol start=\"2\">\n<li>Supplementary angles: Two angles are said to be supplementary if the sum of their degree measure is 180\u00b0.<br \/>\u2220AOC + \u2220BOC = 180\u00b0<\/li>\n<li>Bisector of angle: A ray that divides an angle into two equal parts is called a bisector of the angle.<br \/>\u2220AOC = \u2220BOC<\/li>\n<li>Adjacent angles: Two angles are said to be adjacent angles if<\/li>\n<\/ol>\n<ul>\n<li>They have a common vertex (O)<\/li>\n<li>They have a common arm (OC)<\/li>\n<li>and their non-common arms are on either side of the common arm (OA and OB).<br \/>\u2220AOB = \u2220AOC +\u2220BOC<\/li>\n<\/ul>\n<ol start=\"5\">\n<li>Linear pair: Two adjacent angles are said to be linear pair if their sum is equal to 180\u00b0.<br \/>\u2220AOC + \u2220BOC = 180\u00b0<br \/>Axiom 6.1: If a ray stands on a line, then the sum of two adjacent angles so formed is 180\u00b0.<br \/>Axiom 6.2: If the sum of two adjacent angles is 180\u00b0, then the non-common arms of the angles form a line.<\/li>\n<li>Vertically opposite angles: Vertically opposite angles are those angles that are opposite to each other (or not adjacent) when two lines cross each other.<br \/>Theorem 6.1: If two lines intersect each other, then the vertically opposite angles are equal.<br \/>To prove: If lines AB and CD mutually intersect at point O, then<br \/>(a) \u2220AOC = \u2220BOD (Vertically opposite angles)<br \/>(b) \u2220AOD = \u2220BOC<\/li>\n<\/ol>\n<p>RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions: Proof: Lines AB intersect CD at O.<br \/>\u22201 + \u22202 = 180\u00b0 (Linear pair)<br \/>\u22202 + \u22203 = 180\u00b0 (Linear pair)<br \/>From eqn. (1) and (2), \u22201 + \u22202 = \u22202 + \u22203<br \/>\u21d2 \u22201 = \u22203 \u21d2 \u2220AOD = \u2220BOC<br \/>Similarly, \u2220AOC = \u2220BOD<\/p>\n<p>Parallel Lines<br \/>If the distance between two lines is the same at each and every point on two lines, then two lines are said to be parallel.<br \/>If lines l and m do not intersect each other at any point then l || m.<\/p>\n<p>Transversal line: A line is said to be transversal which intersects two or more lines at distinct points.<\/p>\n<ol>\n<li>Corresponding angles: A pair of angles having different vertex but lying on the same side of the transversal are called corresponding angles. Note that in each pair one is interior and other is exterior angle.<\/li>\n<\/ol>\n<ul>\n<li>\u22201 and \u22202<\/li>\n<li>\u22203 and \u22204<\/li>\n<li>\u22205 and \u22206<\/li>\n<li>\u22201 and \u22208<\/li>\n<\/ul>\n<p>These angles are pair of corresponding angles.<\/p>\n<ol start=\"2\">\n<li>Alternate interior angles: Pair of angles having distinct vertices and lying can either side of the transversal are called alternate interior angles.<\/li>\n<\/ol>\n<ul>\n<li>\u22201 and \u22202<\/li>\n<li>\u22203 and \u22204<\/li>\n<\/ul>\n<p>These angles are alternate interior angles<\/p>\n<ol start=\"3\">\n<li>Consecutive interior angles: Pair of interior angles of the same side of the transversal line.<\/li>\n<\/ol>\n<ul>\n<li>\u22201 and \u22202<\/li>\n<li>\u22202 and \u22204<\/li>\n<\/ul>\n<p>These angles are consecutive interior angles or co-interior angles<\/p>\n<p>Axiom 6.3: If two parallel lines are intersected by a transversal then each pair of corresponding angles are equal.<br \/>If AB || CD, then<\/p>\n<ul>\n<li>\u2220PEB = \u2220EFD<\/li>\n<li>\u2220PEA = \u2220EFC<\/li>\n<li>\u2220BEF = \u2220DFQ<\/li>\n<li>\u2220AEF = \u2220CFQ<\/li>\n<\/ul>\n<p>Theorem 6.2: If two parallel lines are intersected by a transversal then pair of alternate interior angles are equal.<br \/>If AB || CD, then ?<\/p>\n<ul>\n<li>\u2220AEF = \u2220EFD<\/li>\n<li>\u2220BEF = \u2220CFE<\/li>\n<\/ul>\n<p>Theorem 6.3: If two parallel lines are intersected by a transversal then the ! sum of consecutive interior angles of the same side of transversal is equal to 180\u00b0. If AB || CD then<br \/>(i) \u2220BEF + \u2220DFE = 180\u00b0<br \/>(ii) \u2220AEF + \u2220CFE = 180\u00b0<\/p>\n<p>Axiom 6.4: If two lines are intersected by a transversal and a pair of corresponding angles are equal, then two lines are parallel.<br \/>(i) If \u2220PEB = \u2220EFD (corresponding angles), then AB || CD<br \/>Theorem 6.4: If two lines intersected by a transversal and a pair of alternate interior angles are equal, then two lines are parallel. If \u2220AEF = \u2220EFD (alternate interior angles), then AB || CD.<\/p>\n<p>Theorem 6.5: If two lines are intersected by a transversal and the sum of consecutive interior angles of same side of transversal is equal to 180\u00b0, the lines are parallel. If \u2220AEF + \u2220CFE = 180\u00b0, then AB || CD.<\/p>\n<p>Theorem 6.6: Lines which are parallel to the same line are parallel to each other.<br \/>If AB || EF and CD || EF then AB || CD<\/p>\n<p>Theorem 6.7: The sum of the angles of a triangle is equal to 180\u00b0.<br \/>Given: \u0394ABC<br \/>To prove: \u2220A + \u2220B + \u2220C = 180\u00b0<br \/>Construction: Draw DE || BC<br \/>Proof: DE || BC<br \/>then \u22201 = \u22204 \u2026(1) (alternate interior angles)<br \/>\u22202 = \u22205 \u2026(2) (alternate interior angles)<br \/>Adding equations (1) and (2),<br \/>\u22201 + \u22202 = \u22204 +\u22205<br \/>Adding \u22203 on both sides,<br \/>\u22201 +\u22202 + \u22203 = \u22203 + \u22204 + \u22205<br \/>\u21d2 \u2220A + \u2220B + \u2220C = 180\u00b0 (Sum of angles at a point on same side of a line is 180\u00b0)<\/p>\n<p>Theorem 6.8: If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.<br \/>Given: AABC in which, side BC is produced to D.<br \/>To Prove: \u2220ACD = \u2220BAC + \u2220ABC<br \/>Proof: \u2220ACD + \u2220ACB = 180\u00b0 \u2026(1) (Linear pair)<br \/>\u2220ABC + \u2220ACB + \u2220BAC = 180\u00b0 \u2026(2)<br \/>From eqn. (1) and (2), \u2220ACD + \u2220ACB<br \/>= \u2220ABC + \u2220ACB + \u2220BAC<br \/>= \u2220ACD = \u2220ABC + \u2220BAC<\/p>\n<p>Now we have covered RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions. It is advised to go through it thoroughly to understand it better.<\/p>\n<p>Know more at the <a href=\"https:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener\">official website<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>RS Aggarwal Chapter 7 Class 9 Maths Exercise 7.1 Solutions: You have also studied some axioms and, with the help of these axioms, you proved some other statements. In this chapter, you will study the properties of the angles formed when two lines intersect each other, and also the properties of the angles formed when &#8230; <a title=\"RS Aggarwal Chapter 7 Class 9 Maths Exercises 7.1 (ex 7a) Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-7-class-9-maths-exercise-7-1-solutions\/\" aria-label=\"More on RS Aggarwal Chapter 7 Class 9 Maths Exercises 7.1 (ex 7a) Solutions\">Read more<\/a><\/p>\n","protected":false},"author":236,"featured_media":67361,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[1,73395,73412,2985,73410],"tags":[3081,3086,4711],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/67271"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/236"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=67271"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/67271\/revisions"}],"predecessor-version":[{"id":523025,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/67271\/revisions\/523025"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/67361"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=67271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=67271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=67271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}