Chapter 4.1, Problem 10CE

To determine

ToProve : Prove that $\overline{DC}\left|\right|\overline{AB}$ in the figure shown below.

Explanation of Solution

Given information : Two triangle are congruent shown in the figure given below

  

Formula used: When two lines are cut by a transversal line and if the alternate interior angles are equal then lines are parallel.

Proof :

Given that two triangle is congruent.

i.e. $\Delta ABO\cong \Delta CDO$

We know that when two triangles are congruent then their corresponding angles and sides are equal.

So, we have

  $\angle A=\angle C$ and $\angle B=\angle D$

We know that when a parallel line cut by a transversal line then alternate interior angle is equal.

Here, $\angle A=\angle C$

This imply that $\overline{DC}\left|\right|\overline{AB}$ and AC is a transversal line.