Answer
$C$
Work Step by Step
In a right triangle, the altitude splits the large triangle into two other right triangles, and all three triangles are similar to one another.
Let's write the angle congruence statements. We'll start with the right angles:
$\angle BCA ≅ \angle CDB ≅ \angle CDA$
Let's look at the next largest angles:
$\angle DCB ≅ \angle A ≅ \angle A$
Finally, let's look at the smallest angles:
$\angle B ≅ \angle DCA ≅ \angle B$
According to these congruence statements, $\angle DCB ≅ \angle A$. The answer is option $C$.
