Answer
The triangle might be an equilateral triangle.
False
The triangle must be a right triangle.
False
The triangle might be an acute triangle.
True
Step-by-step explanation
First of, we will explain the different types of triangles that exist based on side lengths and angle measures respectively,
Based on side lengths,
- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.
- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.
- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.
Based on angle measures,
- Acute triangle has all of the angles in the triangle being less than 90 degrees.
- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.
- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.
So, a sketch of the triangle described would look like
So, we can see that the triangle has two sides equal, hence, the two base angles will be equal to.
If we call those base angles, x,
x + x + 45° = 180°
2x = 180° - 45°
2x = 135°
Divide both sides by 2
(2x/2) = (135°/2)
x = 67.5°
Three angles of the triangle are 45°, 67.5° and 67.5°
So, taking the statements one at a time now
The triangle might be an equilateral triangle.
This statement is False since it is evident that all the angles of this triangle are not equal to one another, hence, the sides cannot all be equal too.
The triangle must be a right triangle.
This statement too, is False. None of the angles of the triangle is equal to 90°.
The triangle might be an acute triangle.
This statement is True. All of the angles of the triangle are less than 90°.
Hope this Helps!!!