Question

Given: $\overline{BE}\perp \overline{DA};\overline{CD}\perp \overline{DA}$

Prove: $\angle 1\cong \angle 2$

Short answer

The conclusion is that $\angle 1\cong \angle 2$.

Step-by-step solution

Step 1. Determine the theorem or postulate that can be used

The theorem 3-7 can be used which states that it can be said that the relation between two lines is parallel when both the lines are having a perpendicular relation with the same line.

The theorem 3-2 can be used which states that if the relation between two lines is parallel only and a separate line travels through these two lines then the angles which are positioned on the alternate interior side represents the congruent angles.

Step 2. Use the theorem 3-7

Determine the lines that are having a parallel relation between them by using the provided relation between the lines and theorem 3-7.

$\overline{CD}||\overline{BE}$

Step 3. Make the conclusion

According to the provided figure a separate line is travelling through the obtained parallel lines then use theorem 3-2 to determine the angles associated with these lines and their relation with each other.

$\angle 1\cong \angle 2$