Question

Select the statements that, when taken alone, could be used to prove that HIN and TIG are similar.

a) The angles of HIN and TIG are all congruent.
b) The sides of HIN and TIG are all proportional.
c) HIN and TIG have the same perimeter.
d) The area of HIN is equal to the area of TIG.

Answer 1

To prove that HIN and TIG are similar, you need to show congruent angles and proportional sides. Statement a) states that the angles of HIN and TIG are congruent, which is one criterion for similarity. Statements a) and c) together are sufficient to prove similarity.

Step-by-step explanation:

To prove that HIN and TIG are similar, we need to show that the corresponding angles are congruent and the corresponding sides are proportional. Statement a) states that the angles of HIN and TIG are all congruent, which is one of the criteria for similarity. So, statement a) can be used to prove that HIN and TIG are similar. However, statement b) about the sides being proportional alone is not enough to prove similarity. We need both angles and sides to be congruent or proportional to establish similarity. Therefore, statements a) and c) together can be used to prove that HIN and TIG are similar because a) establishes congruent angles and c) establishes equal perimeters.