{"id":9422,"date":"2023-05-30T17:47:16","date_gmt":"2023-05-30T12:17:16","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=9422"},"modified":"2023-05-31T17:22:32","modified_gmt":"2023-05-31T11:52:32","slug":"ap-ssc-10th-class-maths-notes-chapter-8","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-ssc-10th-class-maths-notes-chapter-8\/","title":{"rendered":"AP SSC 10th Class Maths Notes Chapter 8 Similar Triangles"},"content":{"rendered":"

Students can go through AP SSC 10th Class Maths Notes<\/a> Chapter 8 Similar Triangles to understand and remember the concepts easily.<\/p>\n

AP State Syllabus SSC 10th Class Maths Notes Chapter 8 Similar Triangles<\/h2>\n

\u2192 The geometrical figures which have the same shape but are not necessarily of the same size are called similar figures.<\/p>\n

\u2192 The heights and distances of distant objects can be found using the principles of similar figures.<\/p>\n

\u2192 Two polygons with same number of sides are said to be similar if their corresponding angles are equal and their corresponding sides are in proportion.<\/p>\n

\u2192 A polygon in which all sides and all its angles are equal is called a regular polygon. Eg.:
\n\"AP<\/p>\n

\"AP<\/p>\n

\u2192 The ratio of the corresponding sides is referred to as scale factor or representative factor.<\/p>\n

\u2192 All squares are similar.<\/p>\n

\u2192 All circles are similar.<\/p>\n

\u2192 All equilateral triangles are similar.<\/p>\n

\u2192 Two congruent figures are similar but two similar figures need not be congruent.<\/p>\n

\u2192 A square ABCD and a rectangle PQRS are of equal corresponding angles, but their corre\u00acsponding sides are not in proportion.
\n\"AP
\n\u2234 The square ABCD and the rectangle PQRS are not similar.<\/p>\n

\u2192 The corresponding sides of a square ABCD and a rhombus PQRS are equal but their corresponding angles are not equal. So they are not similar.
\n\"AP<\/p>\n

\u2192 If a line is drawn parallel to one side of a triangle intersecting the other two sides at two distinct points then the other two sides are divided in the same ratio.
\n\"AP
\nIn \u25b3ABC; DE \/\/ BC then \\(\\frac{AD}{DB}\\) = \\(\\frac{AE}{EC}\\).
\nThis is called Basic proportionality theorem (or) Thale\u2019s theorem.<\/p>\n

\"AP<\/p>\n

\u2192 If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.
\n\"AP
\nIn \u25b3ABC, a line ‘l’ intersecting AB in D and AC in E
\nsuch that \\(\\frac{AD}{DB}\\) = \\(\\frac{AE}{EC}\\) then l \/\/ BC.
\nThis is converse of Thale\u2019s theorem.<\/p>\n

\u2192 Two triangles are similar, if
\ni) their corresponding angles are equal.
\nii) their corresponding sides are in the same ratio.<\/p>\n

\u2192 If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio or proportional and hence the two triangles are similar.
\n\"AP
\nIn \u25b3ABC, \u25b3DEF
\n\u2220A = \u2220D
\n\u2220B = \u2220E
\n\u2220C = \u2220F
\n\u21d2 \\(\\frac{AB}{DE}\\) = \\(\\frac{BC}{EF}\\) = \\(\\frac{AE}{DF}\\)
\n\u2234 \u25b3ABC ~ \u25b3DEF (A.A.A)<\/p>\n

\"AP<\/p>\n

\u2192 If in two triangles, sides of one triangle are proportional to the sides of other triangle, then their corresponding angles are equal and hence the two triangles are similar.
\n\"AP
\nIn \u25b3ABC, \u25b3DEF
\nif \\(\\frac{AB}{DE}\\) = \\(\\frac{BC}{EF}\\) = \\(\\frac{AE}{DF}\\)
\n\u21d2 \u2220A = \u2220D
\n\u2220B = \u2220E
\n\u2220C = \u2220F
\nHence, \u25b3ABC ~ \u25b3DEF (S.S.S)<\/p>\n

\u2192 If two angles of a triangle are equal to two corresponding angles of another triangle then the two triangles are similar.
\n\"AP
\nIn \u25b3ABC, \u25b3DEF
\nif \u2220A = \u2220D
\n\u2220B = \u2220E
\n\u21d2 \u2220C = \u2220F (By Angle Sum property)
\n\u2234 \u25b3ABC ~ \u25b3DEF (A.A)<\/p>\n

\u2192 If one angle of a triangle is equal to one angle of other triangle and the sides including these angles are proportional, then the two triangles are similar.
\n\"AP
\nIn \u25b3ABC, \u25b3DEF if \u2220A = \u2220D, and
\n\\(\\frac{AB}{DE}\\) = \\(\\frac{AC}{DF}\\)
\n\u21d2 \u25b3ABC ~ \u25b3DEF (S.A.S)<\/p>\n

\"AP<\/p>\n

\u2192 The ratio of areas of two similar triangles is equal to the ratio corresponding sides.
\n\"AP
\n\"AP<\/p>\n

\u2192 If a perpendicular is drawn from the vertex, containing the right angle of a right angled – triangle to the hypotenuse, then the triangles on each side of perpendicular are similar to one another and to the original triangle. Also the square of the perpendicular is equal to the product of the lengths of the two parts of the hypotenuse.
\nIn \u25b3ABC, \u2220B = 90\u00b0
\nBD \u22a5 AC
\n\"AP
\nThen \u25b3ADB ~ \u25b3BDC ~ \u25b3ABC and
\nBD2<\/sup> = AD . DC<\/p>\n

\u2192 Pythagoras theorem: In a right angled triangle, the square of hypotenuse is equal to the sum of the squares of other two sides.
\n\"AP
\nIn \u25b3ABC; \u2220A = 90\u00b0
\nAB2<\/sup> + AC2<\/sup> = BC2<\/sup><\/p>\n

\u2192 In a triangle, if square of one side is equal to sum of squares of the other two sides, then the angle opposite to the first side is right angle.
\n\"AP
\nIn \u25b3ABC, if
\nAC2<\/sup> = AB2<\/sup> + BC2<\/sup> then \u2220B = 90\u00b0
\nThis is converse of Pythagoras theorem.<\/p>\n

\"AP<\/p>\n

\u2192 Baudhayan Theorem (about 800 BC):
\nThe diagonal of a rectangle produces itself the same area as produced by its both sides (i.e., length and breadth).
\nIn rectangle ABCD,
\n\"AP
\narea produced by the diagonal AC = AC \u2022 AC
\n= AC2<\/sup>
\narea produced by the length = AB \u2022 BA = AB
\narea produced by the breadth = BC \u2022 CB = BC2<\/sup>
\nHence, AC2<\/sup> = AB2<\/sup> + BC2<\/sup>.<\/p>\n

\u2192 A sentence which is either true or false but not both is called a simple statement.<\/p>\n

\u2192 A statement formed by combining two or more simple statements is called a compound statement.<\/p>\n

\u2192 A compound statement of the form “If …… then ……\u201d is called a Conditional or Implication.<\/p>\n

\u2192 A statement obtained by modifying the given statement by \u2018NOT\u2019 is called its negation.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can go through AP SSC 10th Class Maths Notes Chapter 8 Similar Triangles to understand and remember the concepts easily. AP State Syllabus SSC 10th Class Maths Notes Chapter 8 Similar Triangles \u2192 The geometrical figures which have the same shape but are not necessarily of the same size are called similar figures. \u2192 … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/9422"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=9422"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/9422\/revisions"}],"predecessor-version":[{"id":40858,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/9422\/revisions\/40858"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=9422"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=9422"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=9422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}