Use the image to answer the question.
An illustration shows two similar triangles.
On triangle A B C, side A C measures 16, side A B measures 22, and side B C measures 24. Angle A measures 77 degrees, angle B measures 40 degrees, and angle C measures 63 degrees. On triangle D E F, side F D measures 8, side D E measures 11, and side E F measures 12. Angle D measures 77 degrees, angle E measures 40 degrees, and angle F measures 63 degrees.
ΔABC is similar to ΔDEF . Find the ratio between ΔDEF and ΔABC . Express the answer as a fraction in simplest form.
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To solve this problem, we need to use the concept of similarity of triangles.
Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportional lengths. In this case, we are given that ΔABC is similar to ΔDEF.
To find the ratio between the two triangles, we need to compare the lengths of the corresponding sides. In ΔABC, side AC measures 16, side AB measures 22, and side BC measures 24. In ΔDEF, side FD measures 8, side DE measures 11, and side EF measures 12.
We can now compare the corresponding sides:
AC/FD = 16/8 = 2
AB/DE = 22/11 = 2
BC/EF = 24/12 = 2
Since the ratio of corresponding sides is the same for all sides, the ratio between ΔDEF and ΔABC is 2/2, which simplifies to 1/1.
Therefore, the ratio between ΔDEF and ΔABC is 1:1.
To find the ratio between ΔDEF and ΔABC, we can compare the corresponding side lengths of the two triangles.
In ΔABC, we can see that side AC is 16, side AB is 22, and side BC is 24.
In ΔDEF, side FD is 8, side DE is 11, and side EF is 12.
To find the ratio between the two triangles, we can divide the corresponding side lengths.
Ratio of side lengths:
AC/FD = 16/8 = 2
AB/DE = 22/11 = 2
BC/EF = 24/12 = 2
Since the ratios for all the corresponding sides are equal, we can conclude that the ratio between ΔDEF and ΔABC is 2/2, which simplifies to 1/1. Therefore, the ratio between ΔDEF and ΔABC is 1:1.
Apologies for the incorrect response.
To find the ratio between ΔDEF and ΔABC, we can compare the lengths of their corresponding sides. Looking at the image, we can see that side AC in ΔABC is similar to side DE in ΔDEF. Similarly, side AB in ΔABC is similar to side DF in ΔDEF, and side BC in ΔABC is similar to side EF in ΔDEF.
Using the corresponding side lengths, we can set up the following ratios:
AC/DE = 16/11
AB/DF = 22/8
BC/EF = 24/12
To simplify the ratios, we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case.
So, the simplified ratios are:
AC/DE = 16/11
AB/DF = 11/4
BC/EF = 2
Therefore, the ratio between ΔDEF and ΔABC is 16/11 : 11/4 : 2, which can also be simplified as 64/11 : 11/4 : 2.