Eric drew an obtuse triangle which of the following could be true
-The triangle has three unequal sides
-The triangle has two acute angles
-The triangle has one obtuse angle
To determine if a triangle is obtuse, we need to check the measures of its angles. In an obtuse triangle, one of the angles will be greater than 90 degrees.
Here are some possible scenarios for Eric's obtuse triangle:
1. The triangle has angle measures of 100°, 40°, and 40°. In this case, one angle (100°) is greater than 90°, making the triangle obtuse.
2. The triangle has angle measures of 80°, 70°, and 70°. Although none of the angles individually exceeds 90°, the sum of the two smaller angles (70° + 70° = 140°) is greater than 90°, making the triangle obtuse.
3. The triangle has angle measures of 110°, 35°, and 35°. Similar to the previous scenario, the sum of the two smaller angles (35° + 35° = 70°) is less than 90°, while the largest angle (110°) is greater than 90°, making the triangle obtuse.
These are just a few examples of obtuse triangles. There can be many other combinations of angle measures that would result in an obtuse triangle.
To determine which statements could be true about Eric's obtuse triangle, we need to understand what an obtuse triangle is. An obtuse triangle is a triangle that has one angle greater than 90 degrees.
When considering the options, we need to ensure that at least one angle in each triangle is greater than 90 degrees. Let's evaluate the options:
A) All angles are acute: This option cannot be true because in an obtuse triangle, at least one angle must be greater than 90 degrees.
B) Exactly one angle is obtuse: This option could be true as it aligns with the definition of an obtuse triangle. If one angle in the triangle is greater than 90 degrees while the others are acute, it would be an obtuse triangle.
C) Two angles are obtuse: This option cannot be true because the sum of the angles in a triangle is always 180 degrees. If two angles were obtuse (greater than 90 degrees), their sum would be greater than 180 degrees, which contradicts the definition of a triangle.
D) All angles are obtuse: This option cannot be true because, as mentioned before, the sum of the angles in a triangle is always 180 degrees. If all angles were obtuse, their sum would be greater than 180 degrees, making it impossible for them to form a triangle.
Therefore, the statement "Exactly one angle is obtuse" is the only option that could be true for Eric's obtuse triangle.