Question

In δdef, m∠d = 117° and m∠e = 26°. which list has the sides of δdef in order from shortest to longest?

A) DE,EF,FD
B) EF,FD,DE
C) FD,DE,EF
D) DE,FD,EF

Answer 1

To list the sides of ΔDEF from shortest to longest, we use the triangle's angles, with m∠D = 117° and m∠E = 26°. By calculating m∠F, we determine that side FD is shortest, DE is of medium length, and EF is the longest, making option B) EF,FD,DE the correct answer.

Step-by-step explanation:

To list the sides of ΔDEF in order from shortest to longest, we can use the fact that in any triangle, the side opposite the smallest angle is the shortest, and the side opposite the largest angle is the longest. In ΔDEF, we have m∠D = 117° and m∠E = 26°. Since the sum of angles in any triangle is 180°, we can find the measure of angle F by subtracting the measures of angles D and E from 180°:

m∠F = 180° - m∠D - m∠E = 180° - 117° - 26° = 37°.

Now we can see that m∠E is the smallest angle, so side FD opposite ∠E will be the shortest. Next, m∠F is larger than m∠E but smaller than m∠D, so side DE opposite ∠F will be of medium length. Finally, m∠D is the largest angle, so side EF opposite ∠D will be the longest. Therefore, the sides of ΔDEF in order from shortest to longest are FD, DE, and EF, which corresponds to option B).