Page 1 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2 . If EF = 15.4 cm, find BC. Answer 1: Page 2 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2 . If EF = 15.4 cm, find BC. Answer 1: Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 Question 2: Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD. Answer 2: Since AB || CD, ? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles) In ?AOB and ?COD, ?AOB = ?COD (Vertically opposite angles) ?OAB = ?OCD (Alternate interior angles) ?OBA = ?ODC (Alternate interior angles) ? ?AOB ~ ?COD (By AAA similarity criterion) Page 3 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2 . If EF = 15.4 cm, find BC. Answer 1: Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 Question 2: Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD. Answer 2: Since AB || CD, ? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles) In ?AOB and ?COD, ?AOB = ?COD (Vertically opposite angles) ?OAB = ?OCD (Alternate interior angles) ?OBA = ?ODC (Alternate interior angles) ? ?AOB ~ ?COD (By AAA similarity criterion) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 3 Question 3: In the following figure, ABC and DBC are two triangles on the same base BC. If AD Answer 3: Let us draw two perpendiculars AP and DM on line BC. In ?APO and ?DMO, ?APO = ?DMO (Each = 90°) ?AOP = ?DOM (Vertically opposite angles) ? ?APO ~ ?DMO (By AA similarity criterion) intersects BC at O, show that We know that area of a triangle = . Page 4 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2 . If EF = 15.4 cm, find BC. Answer 1: Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 Question 2: Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD. Answer 2: Since AB || CD, ? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles) In ?AOB and ?COD, ?AOB = ?COD (Vertically opposite angles) ?OAB = ?OCD (Alternate interior angles) ?OBA = ?ODC (Alternate interior angles) ? ?AOB ~ ?COD (By AAA similarity criterion) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 3 Question 3: In the following figure, ABC and DBC are two triangles on the same base BC. If AD Answer 3: Let us draw two perpendiculars AP and DM on line BC. In ?APO and ?DMO, ?APO = ?DMO (Each = 90°) ?AOP = ?DOM (Vertically opposite angles) ? ?APO ~ ?DMO (By AA similarity criterion) intersects BC at O, show that We know that area of a triangle = . Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 4 Question 4: If the areas of two similar triangles are equal, prove that they are congruent. Answer 4: Let us assume two similar triangles as ?ABC ~ ?PQR. Question 5: D, E and F are respectively the mid-points of sides AB, BC and CA of ?ABC. Find the ratio of the area of ?DEF and ?ABC. Answer 5: D and E are the mid-points of ?ABC. Page 5 Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 1 Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2 . If EF = 15.4 cm, find BC. Answer 1: Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 2 Question 2: Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD. Answer 2: Since AB || CD, ? ?OAB = ?OCD and ?OBA = ?ODC (Alternate interior angles) In ?AOB and ?COD, ?AOB = ?COD (Vertically opposite angles) ?OAB = ?OCD (Alternate interior angles) ?OBA = ?ODC (Alternate interior angles) ? ?AOB ~ ?COD (By AAA similarity criterion) Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 3 Question 3: In the following figure, ABC and DBC are two triangles on the same base BC. If AD Answer 3: Let us draw two perpendiculars AP and DM on line BC. In ?APO and ?DMO, ?APO = ?DMO (Each = 90°) ?AOP = ?DOM (Vertically opposite angles) ? ?APO ~ ?DMO (By AA similarity criterion) intersects BC at O, show that We know that area of a triangle = . Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 4 Question 4: If the areas of two similar triangles are equal, prove that they are congruent. Answer 4: Let us assume two similar triangles as ?ABC ~ ?PQR. Question 5: D, E and F are respectively the mid-points of sides AB, BC and CA of ?ABC. Find the ratio of the area of ?DEF and ?ABC. Answer 5: D and E are the mid-points of ?ABC. Mathematics (www.tiwariacademy.com) (Chapter – 6) (Triangles) (Class – X) www.tiwariacademy.com 5 Question 6: Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.Read More

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