These two scalene triangles are similar with a scale of 5:2. What is true about these figures?
A. a/e = 1
B AB/DE = 2/5
C AC/DF = 5/2
D c/f = 5/2
assuming that ABC ~ DEF in the ratio 5:2, then
AC/DF = 5/2
angles are congruent in similar figures.
It is AC/DF = 5/2
To determine what is true about the similar triangles, let's break down the information provided.
We are given that the two scalene triangles are similar with a scale of 5:2. This means that corresponding sides of the two triangles have a ratio of 5:2.
Let's label the sides of the first triangle as a, b, and c, and the sides of the second triangle as d, e, and f.
Using the given ratio, we can write the following proportions:
a/d = 5/2 (since the ratio of corresponding sides is 5:2)
b/e = 5/2 (since the ratio of corresponding sides is 5:2)
c/f = 5/2 (since the ratio of corresponding sides is 5:2)
Now, let's analyze the answer choices:
A. a/e = 1: This statement is not true, as the ratio of a to e is 5:2, not 1.
B. AB/DE = 2/5: This statement is not true either, as the ratio of AB to DE is not provided in the information given.
C. AC/DF = 5/2: This statement is true, as AC corresponds to DF and the ratio of AC to DF is indeed 5:2.
D. c/f = 5/2: This statement is true, as c corresponds to f and the ratio of c to f is indeed 5:2.
Therefore, the correct answers are options C and D.
To determine what is true about the two similar scalene triangles, we can use the concept of corresponding sides in similar triangles.
In similar triangles, corresponding sides are proportional. This means that if we have two corresponding sides, we can compare their lengths using a ratio.
Given that the scale of the triangles is 5:2, we can compare the lengths of corresponding sides using this ratio.
Let's label the vertices of the first triangle as A, B, and C, and the second triangle as D, E, and F.
The corresponding sides of the triangles are AB and DE, BC and EF, and AC and DF.
Now let's go through each option and see which one is true:
A. a/e = 1: This option doesn't specify any specific sides, so we cannot determine if it's true or not. Therefore, we can rule out option A.
B. AB/DE = 2/5: This option compares the lengths of corresponding sides AB and DE. Since the scale of the triangles is 5:2, this statement is true. Therefore, option B is true.
C. AC/DF = 5/2: This option compares the lengths of corresponding sides AC and DF. Since the scale of the triangles is 5:2, this statement is also true. Therefore, option C is true.
D. c/f = 5/2: This option compares the lengths of corresponding sides BC and EF. It is not comparing AC and DF, as mentioned in the question. Therefore, we cannot determine if it's true or not based on the given information. Hence, we can rule out option D.
In conclusion, the correct answers are options B (AB/DE = 2/5) and C (AC/DF = 5/2).