Chapter 10.1, Problem 15WE

(a)

To determine

To Draw: an acute triangle and bisect each of the three angles.

Explanation of Solution

Given:

An acute angle triangle.

An acute angle triangle is a triangle whose all internal angles less than 90 degrees.

As we know that the angle bisector divides the original angles into two congruent parts.

Thus, an acute angle triangle with angle bisectors as shown below.

  

Here, O is the point of intersection of angle bisectors.

(b)

To determine

To draw: an obtuse triangle and bisect each of the three angles.

Explanation of Solution

Given:

An obtuse angle triangle.

An obtuse angle triangle is a triangle whose one of the internal angles is greater than 90 degrees.

As we know that the angle bisector divides the original angles into two congruent parts.

Thus, an obtuse angle triangle with angle bisectors as shown below.

  

Here, E is the point of intersection of angle bisectors.

(c)

To determine

To comment: about the point of intersection of angle bisector of acute and obtuse triangle.

Answer to Problem 15WE

The point of intersection of angle bisector of acute and obtuse triangle lie inside the triangle, i.e. incenter.

Explanation of Solution

Acute triangle with angle bisectors shown below.

  

Obtuse triangle with angle bisectors shown below.

  

The point of intersection of angle bisector of acute and obtuse triangle lie inside the triangles.

Point is called incenter.