Question
A 30-60-90 triangle is half of which of the following triangles?
Option #1: scalene triangle
Option #2: obtuse triangle
Option #3: equilateral triangle
Option #1: scalene triangle
Option #2: obtuse triangle
Option #3: equilateral triangle
Answers
GPT-4o mini
A 30-60-90 triangle is a specific type of right triangle where the angles measure 30 degrees, 60 degrees, and 90 degrees. To determine which of the given options a 30-60-90 triangle could be considered "half of," we can analyze each option:
1. **Scalene Triangle**: A scalene triangle has all sides of different lengths, and there's no particular relationship to a 30-60-90 triangle. Also, a scalene triangle does not have distinct proportions based on angle measures.
2. **Obtuse Triangle**: An obtuse triangle has one angle that is greater than 90 degrees. Since a 30-60-90 triangle consists only of one right angle (90 degrees) and two acute angles (30 degrees and 60 degrees), it cannot ''half'' an obtuse triangle.
3. **Equilateral Triangle**: An equilateral triangle has all sides equal and all angles measuring 60 degrees. If you take an equilateral triangle and draw an altitude from one vertex to the opposite side, this altitude creates two 30-60-90 triangles. Here the 30-60-90 triangle is indeed half of an equilateral triangle.
Based on this analysis, the correct answer is:
**Option #3: equilateral triangle**.
1. **Scalene Triangle**: A scalene triangle has all sides of different lengths, and there's no particular relationship to a 30-60-90 triangle. Also, a scalene triangle does not have distinct proportions based on angle measures.
2. **Obtuse Triangle**: An obtuse triangle has one angle that is greater than 90 degrees. Since a 30-60-90 triangle consists only of one right angle (90 degrees) and two acute angles (30 degrees and 60 degrees), it cannot ''half'' an obtuse triangle.
3. **Equilateral Triangle**: An equilateral triangle has all sides equal and all angles measuring 60 degrees. If you take an equilateral triangle and draw an altitude from one vertex to the opposite side, this altitude creates two 30-60-90 triangles. Here the 30-60-90 triangle is indeed half of an equilateral triangle.
Based on this analysis, the correct answer is:
**Option #3: equilateral triangle**.