Question

In △ CDE, m∠ C=47° and m∠ D=34°. Which list has the sides of △ CDE in order from shortest to longest?

A. CD, EC, DE
B. DE, CD, EC
C. DE, EC, CD
D. EC, CD, DE
E. EC, DE, CD
F. CD, DE, EC

Answer 1

The sides of triangle CDE in order from shortest to longest are DE, EC, CD, based on the measurements of the angles provided and applying the triangle inequality theorem.

Step-by-step explanation:

The student is asking to list the sides of triangle CDE in order from shortest to longest given the measures of two angles. Since the sum of angles in a triangle is always 180°, we can find the measure of the remaining angle. Adding the two provided angles, we get 47° + 34° = 81°. Therefore, the measure of angle E is 180° - 81° = 99°. Now, according to the triangle inequality theorem, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle. Therefore, side DE, opposite angle C (47°), is the shortest, and side CD, opposite angle E (99°), is the longest. So, side EC is in between. This gives us the order: C. DE, EC, CD.