The problem shown involves understanding the properties of the angle bisectors of a triangle.

Analysis:

The question asks what is true about the angle bisectors in a triangle. Let's break down the concepts:

• Angle Bisectors: These are lines that divide the angles of a triangle into two equal halves.

• Concurrency: This refers to three or more lines intersecting at a single point.

The angle bisectors of any triangle (whether it is acute, obtuse, or right-angled) are always concurrent. The point where they meet is called the incenter, which is the center of the triangle's inscribed circle (the circle that touches all three sides from the inside).

Correct Answer:

• "They are always concurrent."

The angle bisectors of all triangles (acute, obtuse, or right) always meet at a single point—the incenter.

Would you like more details on angle bisectors, concurrency, or any related concepts? Here are some related questions to explore this topic:

1. What is the significance of the incenter in a triangle?
2. How do you construct an angle bisector using a compass and straightedge?
3. Can the incenter lie outside the triangle in any case?
4. How do angle bisectors relate to the incircle of a triangle?
5. What is the difference between angle bisectors and perpendicular bisectors in triangles?

Tip: Remember that the incenter is equidistant from all sides of the triangle, which is why it's the center of the inscribed circle!