Chapter 15.2, Problem 17PSB

To determine

To Justify: The one angle is greater than the other in given figure..

Explanation of Solution

Given:

  $\angle \text{2>}\angle \text{1}$

  

Formula Used:

  $\begin{array}{l}\text{Transitive Property of Triangle}\\ If a < b and b < c ,then a < c.\\ If a \le b and b \le c ,then a \le c.\\ If a > b and b > c ,then a > c.\\ If a \ge b and b \ge c ,then a \ge c.\end{array}$

Exterior Angle Theorem: It states that exterior angle is sum of two interior angle.

Calculation:

  $\begin{array}{l}\angle 1>\angle 3\left(\text{exterior angle inequality theorem}\right)\\ \angle 3>\angle 2\left(\text{exterior angle inequality theorem}\right)\\ \angle 1>\angle 2\left(\text{transitive property of Inequality}\right)\\ \text{By law of trichotomy}\\ \angle \text{2>1 is not proved}\text{.}\end{array}$

Conclusion:

Thus, the required argument is not proved.