For a triangle, list the respective names of the points of concurrency of

Question

perpendicular bisectors of the sides
bisectors of the angles
medians
lines containing the altitudes

Answer 1

For a triangle ABC, the respective points of concurrency are as follows:

1. Perpendicular bisectors of the sides:
The perpendicular bisectors of the sides (AB, BC, and AC) intersect at a single point called the circumcenter (O).

2. Bisectors of the angles:
The bisectors of the angles (∠A, ∠B, and ∠C) intersect at a single point called the incenter (I).

3. Medians:
The medians (lines connecting a vertex to the midpoint of the opposite side) intersect at a single point called the centroid (G). The medians of triangle ABC intersect at the point of concurrence G.

4. Lines containing the altitudes:
The altitudes (perpendicular lines from a vertex to the opposite side) intersect at a single point each. The altitude from vertex A intersects side BC at point D, the altitude from vertex B intersects side AC at point E, and the altitude from vertex C intersects side AB at point F.