Chapter 3, Problem 2RP

To determine

To prove : The congruency of $\overline{AC}$ with respect to $\overline{DB}$ .

Explanation of Solution

Given information :

Here, we have given that $\overline{AC}\perp \overline{BC}$ , $\overline{DC}\perp \overline{BC}$ and $\angle 1\cong \angle 2$

Proof: As, $\overline{AC}$ and $\overline{DC}$ both are perpendicular to $\overline{BC}$ ,

  $\Rightarrow \overline{AC}\cong \overline{DC}$

Now, In $\Delta ABC$ and $\Delta DCB$ ,

  $\overline{AC}\cong \overline{DC}$ (Proved above)

  $\angle 1\cong \angle 2$ (Given)

  $\overline{BC}\cong \overline{BC}$ (Common)

  $\Rightarrow \Delta ABC\cong \Delta DCB$ (By SAS Congruency Rule)

  $\therefore \overline{AC}\cong \overline{DB}$ (By Congruent Parts of Congruent Triangles)