Chapter 4.5, Problem 10CE

To determine

To find: congruent criteria used to prove that the triangles are congruent.

Answer to Problem 10CE

Triangle are congruent by SSS congruence criteria

  $\Delta ABC,\Delta DCB$ is a pair of overlapping triangles.

Explanation of Solution

Given information: $\overline{AB}\cong \overline{DC}$ and $\overline{AC}\cong \overline{DB}$

  

Consider $\Delta ABC,\Delta DCB$

  $\overline{AB}\cong \overline{DC}$ (Given)

  $\overline{AC}\cong \overline{DB}$ (Given)

  $\overline{BC}\cong \overline{CB}$ (common side of $\Delta ABC,\Delta DCB$ )

Therefore,

  $\Delta ABC\cong \Delta DCB$ (SSS congruence criteria)

Also.

Congruent triangles basically overlap each other.

So, $\Delta ABC,\Delta DCB$ is a pair of overlapping triangles.