Q15. - Geometry

Question

$\left(a\right).$ Draw any acute triangle. Bisect each of the three angles.

$\left(b\right).$ Draw any obtuse triangle. Bisect each of the three angles

$\left(c\right).$ What do you notice about the points of intersection of the bisectors in parts  $\left(a\right)$ and $\left(b\right)?$                 

$\left(a\right)$

Step-by-Step Solution

Answer

The figure is,

Step 1. Given information.

An acute angle triangle 

Step 2. Follow the ways.

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.

Step 3. Draw the figure.

Therefore, here $O$is the point of intersection of angle bisectors.
$\left(b\right)$

The figure is,

Step 1. Given information.

An obtuse angle triangle.

Step 2. Follow the ways.

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 obtuse angle triangle with angle bisectors as shown below.

Step 3. Draw the figure.

Therefore, here $E$ is the point of intersection of angle bisectors.

$\left(c\right)$

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

Step 1. Given information.

Points of intersection of the bisectors.

Step 2. Acute triangle with angle bisectors shown below.

Step 3. Obtuse triangle with angle bisectors shown below.

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

Point is called incenter.