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.
(1 point)
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1. 0.1
2. 1.8
3.4
4.6
5.1/2
100% correct!!!
To find the ratio between ΔDEF and ΔABC, we can use the corresponding side lengths of the triangles.
In ΔABC, AC measures 16 and AB measures 22.
In ΔDEF, FD measures 8 and DE measures 11.
Since the triangles are similar, we can set up the following proportion:
AC/FD = AB/DE
Plugging in the values, we get:
16/8 = 22/11
Simplifying the left side, we get:
2 = 22/11
Multiplying both sides by 11, we get:
22 = 22
Therefore, the ratio between ΔDEF and ΔABC is 1:1, or 1/1 as a fraction in simplest form.