Page 1 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.3 Question 1: State which pairs of triangles in the following figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: (i) (ii) (iii) Page 2 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.3 Question 1: State which pairs of triangles in the following figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: (i) (ii) (iii) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 (iv) (v) (vi) Answer 1: (i) ?A = ?P = 60° ?B = ?Q = 80° ?C = ?R = 40° Therefore, ?ABC ~ ?PQR [By AAA similarity criterion] (iii)The given triangles are not similar as the corresponding sides are not proportional. ( ii) Page 3 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.3 Question 1: State which pairs of triangles in the following figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: (i) (ii) (iii) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 (iv) (v) (vi) Answer 1: (i) ?A = ?P = 60° ?B = ?Q = 80° ?C = ?R = 40° Therefore, ?ABC ~ ?PQR [By AAA similarity criterion] (iii)The given triangles are not similar as the corresponding sides are not proportional. ( ii) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 3 (iv)The given triangles are not similar as the corresponding sides are not proportional. (v)The given triangles are not similar as the corresponding sides are not proportional. (vi) In ?DEF, ?D + ?E + ?F = 180º (Sum of the measures of the angles of a triangle is 180º.) 70º + 80º + ?F = 180º ?F = 30º Similarly, in ?PQR, ?P + ?Q + ?R = 180º (Sum of the measures of the angles of a triangle is 180º.) ?P + 80º +30º = 180º ?P = 70º In ?DEF and ?PQR, ?D = ?P (Each 70°) ?E = ?Q (Each 80°) ?F = ?R (Each 30°) ? ?DEF ~ ?PQR [By AAA similarity criterion] Question 2: In the following figure, ?ODC ~ ?OBA, ?BOC = 125° and ?CDO = 70°. Find ?DOC, ?DCO and ?OAB Page 4 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.3 Question 1: State which pairs of triangles in the following figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: (i) (ii) (iii) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 (iv) (v) (vi) Answer 1: (i) ?A = ?P = 60° ?B = ?Q = 80° ?C = ?R = 40° Therefore, ?ABC ~ ?PQR [By AAA similarity criterion] (iii)The given triangles are not similar as the corresponding sides are not proportional. ( ii) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 3 (iv)The given triangles are not similar as the corresponding sides are not proportional. (v)The given triangles are not similar as the corresponding sides are not proportional. (vi) In ?DEF, ?D + ?E + ?F = 180º (Sum of the measures of the angles of a triangle is 180º.) 70º + 80º + ?F = 180º ?F = 30º Similarly, in ?PQR, ?P + ?Q + ?R = 180º (Sum of the measures of the angles of a triangle is 180º.) ?P + 80º +30º = 180º ?P = 70º In ?DEF and ?PQR, ?D = ?P (Each 70°) ?E = ?Q (Each 80°) ?F = ?R (Each 30°) ? ?DEF ~ ?PQR [By AAA similarity criterion] Question 2: In the following figure, ?ODC ~ ?OBA, ?BOC = 125° and ?CDO = 70°. Find ?DOC, ?DCO and ?OAB Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 4 Answer 2: DOB is a straight line. ? ?DOC + ?COB = 180° ? ?DOC = 180°  125° = 55° In ?DOC, ?DCO + ?CDO + ?DOC = 180° (Sum of the measures of the angles of a triangle is 180º.) ? ?DCO + 70º + 55º = 180° ? ?DCO = 55° It is given that ?ODC ~ ?OBA. ? ?OAB = ? OCD [Corresponding angles are equal in similar triangles.] ? ?OAB = 55° Question 3: Diagonals AC and BD of a trapezium ABCD with AB  DC intersect each other at the point O. Using a similarity criterion for two triangles, show that Answer 3: In ?DOC and ?BOA, ?CDO = ?ABO [Alternate interior angles as AB  CD] ?DCO = ?BAO [Alternate interior angles as AB  CD] ?DOC = ?BOA [Vertically opposite angles] Page 5 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.3 Question 1: State which pairs of triangles in the following figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: (i) (ii) (iii) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 (iv) (v) (vi) Answer 1: (i) ?A = ?P = 60° ?B = ?Q = 80° ?C = ?R = 40° Therefore, ?ABC ~ ?PQR [By AAA similarity criterion] (iii)The given triangles are not similar as the corresponding sides are not proportional. ( ii) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 3 (iv)The given triangles are not similar as the corresponding sides are not proportional. (v)The given triangles are not similar as the corresponding sides are not proportional. (vi) In ?DEF, ?D + ?E + ?F = 180º (Sum of the measures of the angles of a triangle is 180º.) 70º + 80º + ?F = 180º ?F = 30º Similarly, in ?PQR, ?P + ?Q + ?R = 180º (Sum of the measures of the angles of a triangle is 180º.) ?P + 80º +30º = 180º ?P = 70º In ?DEF and ?PQR, ?D = ?P (Each 70°) ?E = ?Q (Each 80°) ?F = ?R (Each 30°) ? ?DEF ~ ?PQR [By AAA similarity criterion] Question 2: In the following figure, ?ODC ~ ?OBA, ?BOC = 125° and ?CDO = 70°. Find ?DOC, ?DCO and ?OAB Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 4 Answer 2: DOB is a straight line. ? ?DOC + ?COB = 180° ? ?DOC = 180°  125° = 55° In ?DOC, ?DCO + ?CDO + ?DOC = 180° (Sum of the measures of the angles of a triangle is 180º.) ? ?DCO + 70º + 55º = 180° ? ?DCO = 55° It is given that ?ODC ~ ?OBA. ? ?OAB = ? OCD [Corresponding angles are equal in similar triangles.] ? ?OAB = 55° Question 3: Diagonals AC and BD of a trapezium ABCD with AB  DC intersect each other at the point O. Using a similarity criterion for two triangles, show that Answer 3: In ?DOC and ?BOA, ?CDO = ?ABO [Alternate interior angles as AB  CD] ?DCO = ?BAO [Alternate interior angles as AB  CD] ?DOC = ?BOA [Vertically opposite angles] Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 5 ? ?DOC ~ ?BOA [AAA similarity criterion] Question 4: Show that Answer 4: In ?PQR, ?PQR = ?PRQ ? PQ = PR ………………(i) In the following figure,Read More
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