Question

Which of the following is true:

I. Any three line segments make up a triangle.
II. The interior of a triangle includes its vertices.
III. An equilateral triangle is also isosceles.
IV. No isosceles triangle is obtuse.
a) I and II only
b) II and III only
c) III and IV only
d) I, II, III, and IV

Answer 1

The correct options are III and IV only. Any three line segments do not necessarily make up a triangle, the interior of a triangle includes all the points inside the triangle excluding its vertices, an equilateral triangle is also isosceles, but a triangle can be isosceles and obtuse.

Step-by-step explanation:

The correct option is c) III and IV only.

1. Any three line segments do not necessarily make up a triangle. To form a triangle, the three line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
2. The interior of a triangle includes all the points inside the triangle, including its vertices. The vertices themselves are not part of the interior.
3. An equilateral triangle, which has all three sides of equal length, is also considered an isosceles triangle because an isosceles triangle has at least two sides of equal length.
4. A triangle is obtuse if one of its angles measures more than 90 degrees. It is possible for an isosceles triangle to be obtuse, so the statement is false.