[FREE] In a scalene triangle, is the shortest side opposite the angle with the smallest measure? A. True B. - brainly.com (2025)

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In a scalene triangle, all sides have different lengths, and all angles have different measures. One important property of triangles is that the side opposite the smallest angle is always the shortest side. This is because the larger the angle, the longer the opposite side can stretch.

Let's break it down:

Scalene Triangle Definition: A scalene triangle is a type of triangle where all three sides are of different lengths and, consequently, all three angles are of different measures.
Relationship Between Angles and Sides: In any triangle, each angle has a side opposite it. The larger the angle, the longer the opposite side is, and vice versa. This is because in a triangle, sides and angles are directly related through trigonometric and geometric principles.
Smallest Angle and Shortest Side: The smallest angle in a triangle will always be opposite the shortest side. Similarly, the largest angle will be opposite the longest side.

Therefore, in a scalene triangle, since all angles are different, the shortest side must indeed be opposite the angle with the smallest measure.

So, the statement is:

A. True

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In a scalene triangle, the shortest side is opposite the smallest angle because each triangle adheres to the rule where the larger angle corresponds with a longer side. Thus, the statement is true. The answer is A. True.

Explanation

In a scalene triangle, all three sides are of different lengths, and correspondingly, all angles have different measures. One key property of triangles is that the side opposite the smallest angle is always the shortest side. This relationship can be understood through the following points:

Scalene Triangle Definition: A scalene triangle is one where all three sides are unequal, which also means that their opposite angles are all different from each other.
Relationship Between Angles and Sides: In any triangle, the length of a side is directly related to the measure of the angle opposite it. Specifically, the larger the angle, the longer the side opposite it. Conversely, the smallest angle will have the shortest side opposite it.
Smallest Angle and Shortest Side: Therefore, in a scalene triangle, because of the unique measures of angles, the shortest side is indeed situated opposite the smallest angle. Similarly, the side opposite the largest angle will be the longest.

Thus, the following statement is accurate: The shortest side of a scalene triangle is opposite the angle with the smallest measure.

Therefore, the answer is:

A. True

Examples & Evidence

For instance, consider a scalene triangle with angles measuring 30°, 60°, and 90°. The side opposite the 30° angle will be the shortest side, while the side opposite the 90° angle will be the longest side, illustrating the concept clearly.

The principle that states that in a triangle, the side opposite the larger angle is longer and the side opposite the smallest angle is shorter is a fundamental property of triangles known in geometry. This can be confirmed by various theorems related to triangles, such as the Triangle Inequality Theorem.

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