Question

self - assessment
use the diagram in example 3.

1. if it is given that $overline{pw}$ and $overline{qw}$ are congruent, how can you indicate this in the diagram?
2. name a pair of supplementary angles in the diagram. explain.

use the diagram in example 4.

1. can you assume that plane $s$ intersects plane $t$ at $overleftrightarrow{bc}$? explain.
2. explain how you know that $overleftrightarrow{ab}perpoverleftrightarrow{bc}$.

Explanation:

Step1: Indicate congruent segments

Draw small tick - marks on $\overline{PW}$ and $\overline{QW}$ to show they are congruent.

Step2: Identify supplementary angles

Supplementary angles add up to 180 degrees. If two angles form a straight - line in the diagram, they are supplementary. For example, if $\angle A$ and $\angle B$ form a straight - line, $\angle A+\angle B = 180^{\circ}$, so $\angle A$ and $\angle B$ are a pair of supplementary angles.

Step3: Determine plane intersection

We cannot assume that plane $S$ intersects plane $T$ at $\overrightarrow{BC}$ just by looking at the diagram. We need a clear indication (like a line of intersection drawn) or given information stating that the planes intersect at that line.

Step4: Determine perpendicular lines

We know that $\overrightarrow{AB}\perp\overrightarrow{BC}$ if there is a right - angle symbol at the intersection of the two lines in the diagram or if it is given in the problem's conditions.

Answer:

1. Draw the same number of small tick - marks on $\overline{PW}$ and $\overline{QW}$.
2. Any two angles that form a straight - line in the diagram are supplementary.
3. No, we cannot assume it without further indication or given information.
4. Look for a right - angle symbol or given information stating perpendicularity.