Question

If bisector, median, and altitude are the same segment, then the triangle is

isosceles triangle
scalene triangle
equilateral triangle
right triangle

Answer 1

If the bisector, median, and altitude are the same segment in a triangle, then the triangle must be an isosceles triangle.

Step-by-step explanation:

If the bisector, median, and altitude are the same segment in a triangle, then the triangle must be an isosceles triangle.

To understand why, let's break it down:

• A bisector is a line or segment that divides an angle into two equal parts.
• A median is a line or segment that connects a vertex of a triangle to the midpoint of the opposing side.
• An altitude is a line or segment that is perpendicular to a side and passes through the opposing vertex.

Now, if the bisector, median, and altitude are the same segment, that means the line or segment is dividing the angle into two equal parts, connecting a vertex to the midpoint of the opposing side, and is perpendicular to the side and passes through the opposing vertex all at the same time. This can only happen in an isosceles triangle, where at least two sides are equal in length.