Question

Use any tools to construct an acute scalene triangle and the three perpendicular bisectors, three angle bisectors, three medians, and three altitudes. What do you notice?

Answer 1

Here we have an acute scalene triangle and the three perpendicular bisectors, three angle bisectors, three medians, and three altitudes shown in figure.

In

Findings are

1)Altitudes meets at a common point Z.

2) End point of Median and starting point of perpendicular bisectors are same.

3) Angular bisects meets at a common point.

4) Medians meets at a common point, which is the center point of triangle.

5) Perpendicular bisects meets at a common point.

6) Two adjacent altitudes and 2 adjacent Perpendicular bisects forms a parallelogram.

7) Angular bisects lies between Altitudes and Median for every vertices.