Searches related to what is the answer to Triangle ABC has two sides that measure 12 inches and 16 inches. Which could be the measures of the corresponding sides of a triangle that is similar to triangle ABC? 1. 10 in and 14 in 2. 9 in and 12 in 3. 6 in and 10 in 4. 3 in and 8 in
the ratio of the sides must be
... 12:16 = 3:4 = 6:8 = 9:12
To find the answer to this question, we need to understand the concept of similarity in triangles. Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.
In this case, Triangle ABC has sides measuring 12 inches and 16 inches. We are looking for a triangle that is similar to Triangle ABC, so its corresponding sides must be proportional to the sides of Triangle ABC.
To determine if the given options are proportional, we can calculate the ratios of the corresponding sides. Let's check each option:
1. 10 in and 14 in: The ratio of the corresponding sides is 10/12 = 5/6 and 14/16 = 7/8. These ratios are not equal, so this option is not correct.
2. 9 in and 12 in: The ratio of the corresponding sides is 9/12 = 3/4. This ratio is equal to the ratio of the sides of Triangle ABC, so this option is correct.
3. 6 in and 10 in: The ratio of the corresponding sides is 6/12 = 1/2 and 10/16 = 5/8. These ratios are not equal, so this option is not correct.
4. 3 in and 8 in: The ratio of the corresponding sides is 3/12 = 1/4 and 8/16 = 1/2. These ratios are not equal, so this option is not correct.
Therefore, the correct answer is 2. 9 in and 12 in, as the corresponding sides of this triangle are proportional to the sides of Triangle ABC.