Question

select the correct answer from each drop-down menu. based on the two triangles shown, what can be concluded? an angle opposite the longest side of a triangle is the side. angle. a side opposite the smallest angle of a triangle is the

Explanation:

Step1: Analyze Triangle ABC

In triangle \(ABC\), the sides are \(3\), \(4\), \(6\) and angles are \(26.4^\circ\), \(36.3^\circ\), \(117.3^\circ\). The longest side is \(6\) (opposite \(117.3^\circ\), the largest angle), and the shortest side is \(3\) (opposite \(26.4^\circ\), the smallest angle).

Step2: Analyze Triangle DEF

In triangle \(DEF\), the sides are \(8\), \(8.45\), \(11.94\) and angles are \(42^\circ\), \(45^\circ\), \(93^\circ\). The longest side is \(11.94\) (opposite \(93^\circ\), the largest angle), and the shortest side is \(8\) (opposite \(42^\circ\), the smallest angle).

Step3: Deduce the Relationship

From both triangles, we observe that the angle opposite the longest side is the largest angle, and the angle opposite the smallest side is the smallest angle. Also, the side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest side. So, "An angle opposite the longest side of a triangle is the largest angle. A side opposite the smallest angle of a triangle is the shortest side."

Answer:

An angle opposite the longest side of a triangle is the \(\boldsymbol{\text{largest}}\) angle. A side opposite the smallest angle of a triangle is the \(\boldsymbol{\text{shortest}}\) side.