Question

Given: $\angle C\cong \angle 3;\overline{BE}\perp \overline{DA}$

Prove: $\overline{CD}\perp \overline{DA}$

Short answer

The obtained conclusion is that $\overline{\mathit{C}\mathit{D}}\mathbf{\perp }\overline{\mathit{D}\mathit{A}}$.

Step-by-step solution

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

The postulate 11 can be used which states that the relation between two lines is parallel only when a separate line travels through these two lines and the angles that are corresponding will be congruent .

Theorem 3-4 can be used which states that if two lines which are having a parallel relation crossed by a separate line which makes a perpendicular relation with one of the line then that separate line will also make perpendicular relation with another parallel line.

Step 2. Observe the provided figure and information

According to the figure the given congruent angles are representing the corresponding angles which are associated with the lines $\overline{CD}$and $\overline{BE}$along with this a separate line $\overline{CA}$is travelling through them. According to the postulate 11 the lines $\overline{CD}$and$\overline{BE}$ are having a parallel connection between them.

Step 3. Make the conclusion

Use the obtained parallel lines and provided perpendicular lines to determine another perpendicular lines which are $\overline{CD}$and $\overline{DA}$.