Name the angle of elevation and the angle of depression in the figure below. Compare the measures of these angles. Explain.

Given:

Given that AB and CD are parallel lines.

The line CB makes and angle at B and C.

We need to determine the angle of elevation and the angle of depression.

Angle of elevation:

The upward angle to the line of sight from the horizontal line is called the angle of elevation.

From the given figure, the upward angle from the horizontal line is ∠BCD

Thus, ∠BCD is the angle of elevation.

Angle of depression:

The downward angle to the line of sight from the horizontal line is called the angle of depression.

From the given figure, the downward angle from the horizontal line is ∠ABC

Thus, ∠ABC is the angle of depression.

Comparison of two angles:

The angle of elevation is ∠BCD and the angle of depression is ∠ABC

Comparing the two angles, the angles of elevation and depression are always congruent.

Hence, ∠BCD = ∠ABC

Thus, the angle of elevation and the angle of depression are congruent.