The two statements below are different ways to say that the sides of these similar triangles are proportional.
Complete the equations that go with the statements.
YOU MEAN
1) "The ratio of the corresponding sides of these similar triangles is equal."
Equation:
Side of Triangle 1 / Side of Triangle 2 = Side of Triangle 1 / Side of Triangle 2
2) "The sides of these similar triangles are in the same proportion."
Equation:
Side of Triangle 1 : Side of Triangle 2 = Side of Triangle 1 : Side of Triangle 2
To show that the sides of these similar triangles are proportional, we can use two statements:
1. Statement 1: "The ratio of the corresponding sides of these similar triangles is equal."
To complete the equation for this statement, let's consider two similar triangles, Triangle ABC and Triangle DEF. The corresponding sides are AB and DE, BC and EF, and AC and DF. We can express the ratio of the corresponding sides as follows:
AB/DE = BC/EF = AC/DF
2. Statement 2: "The lengths of the corresponding sides of these similar triangles form a proportion."
To complete the equation for this statement, again, let's consider Triangle ABC and Triangle DEF. We can use the side lengths to form a proportion:
AB/DE = BC/EF = AC/DF
In both cases, the equations express the relationships between the corresponding sides of the similar triangles. By calculating the ratios or forming a proportion, we can determine if the sides are proportional and therefore establish the similarity between the triangles.