{"id":781,"date":"2023-11-06T07:19:00","date_gmt":"2023-11-06T01:49:00","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=781"},"modified":"2023-11-07T17:14:16","modified_gmt":"2023-11-07T11:44:16","slug":"samacheer-kalvi-9th-maths-chapter-4-ex-4-1","status":"publish","type":"post","link":"https:\/\/samacheerguru.com\/samacheer-kalvi-9th-maths-chapter-4-ex-4-1\/","title":{"rendered":"Samacheer Kalvi 9th Maths Solutions Chapter 4 Geometry Ex 4.1"},"content":{"rendered":"

You can Download Samacheer Kalvi 9th Maths Book Solutions<\/a>\u00a0Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 4 Geometry Ex 4.1<\/h2>\n

Question 1.
\nIn the figure, AB is parallel to CD, find x
\n\"Samacheer
\nSolution:
\n(i) From the figure
\n\u22201 = 140\u00b0 (\u2234 corresponding angles are equal)
\n\u22202 = 40\u00b0 (\u2234 \u22201 + \u22202= 180\u00b0)
\n\u22203 = 30\u00b0 (\u2235 \u22203 + 150= 180\u00b0)
\n\u22204 = 110\u00b0 (\u2235 \u22202 + \u22203 + \u22204 = 180\u00b0)
\n\u2234 \u2220x = 70\u00b0 (\u2235 \u22204 + \u2220x = 180\u00b0)
\n\"Samacheer<\/p>\n

(ii) From the figure
\n\u22201 = 48\u00b0
\n\u22203 = 108\u00b0 (\u22201 +24\u00b0 + \u22203 = 180\u00b0)
\n\u22204 = 108\u00b0 (If two lines are intersect, then the vertically the opposite angles are equal)
\n\u22205 = 72\u00b0 (\u2235 \u22203 + \u22205 = 180\u00b0)
\n\u2234 \u22203 + \u22204 + \u22205 = 108\u00b0 + 108\u00b0 + 72\u00b0
\nx = 288\u00b0
\n\"Samacheer<\/p>\n

(iii) From the figure
\n\u2220D = 53\u00b0 ( \u2235 \u2220B and \u2220D are alternate interior angles)
\nSum of the three angles of a triangle is 180\u00b0
\n\u2220x\u00b0 = 180\u00b0- (38\u00b0+ 53\u00b0)
\n= 180\u00b0- 91\u00b0 = 89\u00b0
\n\"Samacheer<\/p>\n

Question 2.
\nThe angles of a triangle are in the ratio 1 : 2 : 3, find the measure of each angle of the triangle.
\nSolution:
\nLet the angles be x, 2x and 3x respectively.
\nSum of the three angles of a triangle = 180\u00b0
\n\"Samacheer
\nThe 3 angles of the triangle are 30\u00b0, 60\u00b0, 90\u00b0.<\/p>\n

Question 3.
\nConsider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say \u2018how\u2019; if they are not congruent say \u2018why\u2019 and also say if a small modification would make them congruent:
\n\"Samacheer
\nSolution:
\n(i) Consider \u2206PQR and \u2206ABC
\nGiven, RQ = BC
\nPQ = AB
\n\u2206ABC is not congruent to \u2206PQR
\nIf PR = AC, then \u2206ABC \u2245 \u2206PQR
\n\"Samacheer<\/p>\n

(ii) Consider \u2206ABD and \u2206BCD for the triangles to be congruent.
\nGiven, AB = DC
\nAD = BC and AB is common side.
\n\u2234 By SSS rule \u2206ABD \u2245 \u2206BCD.
\n\"Samacheer<\/p>\n

(iii) Consider \u2206PXY and \u2206PXz,
\nGiven, XY = XZ
\nPY = PZ and PX is common
\n\u2234 By SSS rule \u2206PXY \u2245 \u2206PXZ.
\n\"Samacheer<\/p>\n

(iv) Consider \u2206OAB and \u2206ODC,
\nGiven, OA = OC
\n\"Samacheer
\n\u2220ABO = \u2220ODC and \u2220AOB = \u2220DOC (vertically opposite angles)
\n\u2234 By AAS rule, AOAB = AODC.<\/p>\n

(v) Consider \u2206AOB and \u2206DOC,
\nGiven, AO = OC
\nOB = OD
\n\"Samacheer
\n\"Samacheer
\nand \u2220AOB = \u2220DOC [vertically opposite angles]
\n\u2234 By SAS rule, \u2206AOB = \u2206DOC.<\/p>\n

(vi) Consider \u2206AMB and \u2206AMC,
\nGiven, AB = AC
\n\"Samacheer
\n\u2220AMB = \u2220AMC = 90\u00b0
\n\u2234 AM is common.
\n\u2234 By RHS rule
\n\u2206AMB \u2245 \u2206AMC.<\/p>\n

Question 4.
\n\u2206ABC and \u2206DEF are two triangles in which AB = DF, \u2220ACB = 70\u00b0, \u2220ABC = 60\u00b0; \u2220DEF = 70\u00b0 and \u2220EDF = 60\u00b0. Prove that the triangles are congruent.
\nSolution:
\n\"Samacheer
\n\u2234 By ASA rule \u2206ABC \u2245 \u2206FDE<\/p>\n

Question 5.
\nFind all the three angles of the \u2206ABC
\n\"Samacheer
\nSolution:
\nExterior angle = Sum of the two opposite interior angles.
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download Samacheer Kalvi 9th Maths Book Solutions\u00a0Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 4 Geometry Ex 4.1 Question 1. In the figure, AB is parallel to CD, find x Solution: (i) From the figure […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[3],"tags":[],"blocksy_meta":"","jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/781"}],"collection":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/comments?post=781"}],"version-history":[{"count":1,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/781\/revisions"}],"predecessor-version":[{"id":54989,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/781\/revisions\/54989"}],"wp:attachment":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/media?parent=781"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/categories?post=781"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/tags?post=781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}