Chapter 15.3, Problem 1PSA

To determine

To Find: The longer side in the given figure.

Answer to Problem 1PSA

  $\overline{AC}>\overline{DF}$

Explanation of Solution

Given:

  $\begin{array}{l}\to \overline{AB}\cong \overline{DE}\\ \to \overline{BC}\cong \overline{EF}\\ \to \angle B>\angle E\end{array}$

  

Concept:

The Hinge Theorem: It states that if two sides of two triangles are congruent and angle of one is greater than the angle of second then the third side of the triangle will be greater than the another.

Calculation:

  $\begin{array}{l}\to \overline{AB}\cong \overline{DE}\left(\text{Given}\right)\\ \to \overline{BC}\cong \overline{EF}\left(\text{Given}\right)\\ \to \angle B>\angle E\\ \text{⇒}\text{Conclusion : }\overline{AC}>\overline{DF}\left(\text{The Hinge theorem or SAS inequaliy theorem}\right)\end{array}$

Conclusion:

Thus the $\overline{AC}>\overline{DF}$