Chapter 5, Problem 15PT

To determine

To Find: The comparison for the given measures.

Answer to Problem 15PT

The hinge theorem shows that $AB<BC$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The given measure is $AB$ and $BC$ .

Calculation:

Consider that when the two sides of the triangle are congruent to the other triangles and the included angle of the first side is larger than the included angle of the second triangle. Then, the third side of the first triangle is larger than the third side of the second triangle.

Then in $\Delta ABD$ and $\Delta CBD$ the reflexive property of the congruence shows that $\overline{DB}\cong \overline{DB}$ . Since, $\overline{DA}\cong \overline{DC}$ and $m\angle ADB<m\angle CDB$ .

Then, the hinge theorem shows that $AB<BC$ .