Eric Drew an obtuse triangle, which of the following could be true for Eric’s triangle
A) All three angles measure less than 90 degrees
B) Two angles measure less than 90 degrees and one angle measures more than 90 degrees
C) All three angles measure more than 90 degrees
D) Two angles measure more than 90 degrees and one angle measures less than 90 degrees
Answer: D) Two angles measure more than 90 degrees and one angle measures less than 90 degrees
To determine which of the following could be true for Eric's triangle, we need to understand the characteristics of an obtuse triangle. An obtuse triangle is a type of triangle that has one angle greater than 90 degrees.
Now, let's examine the options and see which ones could represent Eric's obtuse triangle:
1. All three sides have equal lengths (equilateral triangle): An equilateral triangle has all three angles equal to 60 degrees, which means none of them can be greater than 90 degrees. Therefore, this option is not possible.
2. Two sides have equal lengths (isosceles triangle): An isosceles triangle can have one angle greater than 90 degrees, making it a possible option for Eric's obtuse triangle.
3. All three angles are acute: An acute angle measures less than 90 degrees. If all three angles are acute, none of them can be greater than 90 degrees, so this option is not possible for Eric's obtuse triangle.
4. Two angles are equal: Similar to the second option, if two angles are equal, one of them can be greater than 90 degrees, making it a possible option for Eric's obtuse triangle.
From our analysis, options 2 and 4 could be true for Eric's obtuse triangle.
To determine which of the following could be true for Eric's obtuse triangle, we need to understand the characteristics of an obtuse triangle.
An obtuse triangle is a triangle that has one angle greater than 90 degrees (an acute angle) and two angles that are less than 90 degrees (acute angles).
Therefore, out of the following options, the one that could be true for Eric's triangle is:
- It has one angle measuring 120 degrees and two angles measuring 30 degrees.
This option satisfies the definition of an obtuse triangle, as one angle (120 degrees) is greater than 90 degrees, while the other two angles (both 30 degrees) are less than 90 degrees.