Chapter 15, Problem 36CR

To determine

To Prove: In the given triangle one of its angle is greater than other.

Explanation of Solution

Given:

  $\angle A>\angle C$

  

  $\begin{array}{l}\overline{AD}\cong \overline{DC}\\ \angle ADB<\angle BDC\end{array}$

Formula Used:

SAS Inequality theorem.

  $\begin{array}{l}\text{Reflexive property of congruence: It states that an angle, line segment or shape}\\ \text{ is always congruent to it self}\text{.}\end{array}$

  $\begin{array}{l}\overline{AD}\cong \overline{DC}\\ \angle ADB<\angle BDC\\ BD=BD\left(\text{Reflexive property of congruence}\right)\\ \angle A>\angle C\left(\text{SAS Inequality theorem}\right)\end{array}$