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In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?
- a)One triangle is an enlarged copy of other.
- b)The two triangles are necessarily congruent.
- c)The two triangles are congruent by A.A.A. congruency criterion.
- d)All of the above.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In two triangles, the three angles of one triangle are correspondingly...
If the three angles of a triangle are congruent to corresponding angles of the other, it is an enlarged copy of the triangle.
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In two triangles, the three angles of one triangle are correspondingly...
Explanation:
In geometry, two triangles are said to be congruent if their corresponding sides and angles are equal. However, it is important to note that having corresponding equal angles does not necessarily make the triangles congruent.
Given:
We are given that the three angles of one triangle are correspondingly equal to three angles of another triangle.
Statement to be proved:
We need to determine which of the given options is a correct statement.
Option a) One triangle is an enlarged copy of the other:
This statement implies that one triangle is a scaled-up version of the other. In other words, the sides of one triangle are proportional to the sides of the other triangle. However, the given information does not provide any details about the sides of the triangles, so we cannot conclude that one triangle is an enlarged copy of the other based solely on the given information. Therefore, option a) is not a correct statement.
Option b) The two triangles are necessarily congruent:
This statement implies that the two triangles must be congruent based on the given information. However, having corresponding equal angles does not guarantee congruence. Additional information about the sides or other angles is required to determine congruence. Therefore, option b) is not a correct statement.
Option c) The two triangles are congruent by A.A.A. congruency criterion:
This statement suggests that the triangles are congruent based on the Angle-Angle-Angle (A.A.A.) congruency criterion. According to this criterion, if the three angles of one triangle are equal to the three angles of another triangle, the two triangles are congruent. Therefore, option c) is a correct statement.
Conclusion:
From the given options, only option c) is a correct statement. The two triangles are congruent by the A.A.A. congruency criterion.
In geometry, two triangles are said to be congruent if their corresponding sides and angles are equal. However, it is important to note that having corresponding equal angles does not necessarily make the triangles congruent.
Given:
We are given that the three angles of one triangle are correspondingly equal to three angles of another triangle.
Statement to be proved:
We need to determine which of the given options is a correct statement.
Option a) One triangle is an enlarged copy of the other:
This statement implies that one triangle is a scaled-up version of the other. In other words, the sides of one triangle are proportional to the sides of the other triangle. However, the given information does not provide any details about the sides of the triangles, so we cannot conclude that one triangle is an enlarged copy of the other based solely on the given information. Therefore, option a) is not a correct statement.
Option b) The two triangles are necessarily congruent:
This statement implies that the two triangles must be congruent based on the given information. However, having corresponding equal angles does not guarantee congruence. Additional information about the sides or other angles is required to determine congruence. Therefore, option b) is not a correct statement.
Option c) The two triangles are congruent by A.A.A. congruency criterion:
This statement suggests that the triangles are congruent based on the Angle-Angle-Angle (A.A.A.) congruency criterion. According to this criterion, if the three angles of one triangle are equal to the three angles of another triangle, the two triangles are congruent. Therefore, option c) is a correct statement.
Conclusion:
From the given options, only option c) is a correct statement. The two triangles are congruent by the A.A.A. congruency criterion.
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In two triangles, the three angles of one triangle are correspondingly...
A is correct
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In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?a)One triangle is an enlarged copy of other. b)The two triangles are necessarily congruent.c)The two triangles are congruent by A.A.A. congruency criterion.d)All of the above.Correct answer is option 'A'. Can you explain this answer?
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In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?a)One triangle is an enlarged copy of other. b)The two triangles are necessarily congruent.c)The two triangles are congruent by A.A.A. congruency criterion.d)All of the above.Correct answer is option 'A'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?a)One triangle is an enlarged copy of other. b)The two triangles are necessarily congruent.c)The two triangles are congruent by A.A.A. congruency criterion.d)All of the above.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?a)One triangle is an enlarged copy of other. b)The two triangles are necessarily congruent.c)The two triangles are congruent by A.A.A. congruency criterion.d)All of the above.Correct answer is option 'A'. Can you explain this answer?.
In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?a)One triangle is an enlarged copy of other. b)The two triangles are necessarily congruent.c)The two triangles are congruent by A.A.A. congruency criterion.d)All of the above.Correct answer is option 'A'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?a)One triangle is an enlarged copy of other. b)The two triangles are necessarily congruent.c)The two triangles are congruent by A.A.A. congruency criterion.d)All of the above.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?a)One triangle is an enlarged copy of other. b)The two triangles are necessarily congruent.c)The two triangles are congruent by A.A.A. congruency criterion.d)All of the above.Correct answer is option 'A'. Can you explain this answer?.
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