QuestionComplete this sentence: In a triangle, the angle with the greatest measure is always opposite the A. angle with the smallest measure B. second-longest side C. longest side D. shortest side
Studdy Solution
STEP 1
1. We are dealing with a triangle.
2. We need to determine the relationship between the angles and sides of a triangle.
3. The problem involves identifying the side opposite the angle with the greatest measure.
STEP 2
1. Understand the properties of a triangle.
2. Identify the relationship between angles and sides in a triangle.
3. Determine the correct answer based on the properties.
STEP 3
Understand the properties of a triangle. In any triangle, the sum of the interior angles is . The sides and angles have a specific relationship: larger angles are opposite longer sides, and smaller angles are opposite shorter sides.
STEP 4
Identify the relationship between angles and sides in a triangle. According to the triangle inequality theorem, the side opposite the largest angle is the longest side. This is because the larger the angle, the longer the side opposite it must be to maintain the triangle's shape.
STEP 5
Determine the correct answer based on the properties. The angle with the greatest measure is always opposite the longest side. Therefore, the correct completion of the sentence is:
C. longest side
The angle with the greatest measure is always opposite the:
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