Chapter 13.6, Problem 1C

To determine

To draw: The segments that divide the obtuse triangle into acute triangles.

Explanation of Solution

Given information: An obtuse triangle is divided into acute triangles.

Graph:

An obtuse triangle is formed by two acute angles and an obtuse angle. It is known that measure of an obtuse angle is greater than $90°$ and less than $180°$ .

Draw an obtuse angle triangle ABC. To divide the triangle into acute angle triangle, draw the segment $\text{BD}$ that divides triangle $\text{ABC}$ into two acute triangles $\text{ABD}$ and $\text{BCD}$ as shown below.

  

Figure (1)

Interpretation: From the figure it can be observed that the obtuse angle triangle can be divided into two right angle triangles or two acute angle triangles.