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 two triangles, the three angles of one triangle are correspondingly...
A is correct