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For the following figure, name the longest and the shortest side of the triangle.

Short Answer

Expert verified

The longest side is FDand the shortest side isED.

Step by step solution

01

Step 1. Apply the concept of angles.

From the properties of the triangle, that side opposite to the greater angle is greater and the side opposite to the smaller angle is smaller.

The Sum of all sides of a triangle equals to 180 degrees.

02

Step 2. Check the figure.

Consider the figure ΔDEF.

03

Step 3. Find the angle.

From the figure, the measure of angles are as follows:

E=90F=43

From the angle sum property in a triangle, find the third angle as follows:

role="math" localid="1645697096470" E+F+D=18090+D+43=180B=180133B=47

04

Step 4. Step description.

From the properties of the triangle, that side opposite to the greater angle is greater and the side opposite to the smaller angle is smaller.

Then the greater angle is Eand the side opposite to Eis FDand the smaller angle is Fand the side opposite to Fis ED.

Therefore, the longest side is FDand the shortest side is ED.

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