Question

1
the given diagram represents the construction of a line parallel to $overleftrightarrow{ab}$, passing through point p
which equation must be true?
a. $ph = hi$
b. $ij = pq$
c. $ai = ib$
d. $si = ai$

Explanation:

Step1: Recall parallel line construction

The method to draw a line parallel to $\overleftrightarrow{AB}$ through $P$ uses copying a circular arc of equal radius. The arcs $IJ$ and $PQ$ are drawn with the same compass width, so their lengths (arc measures corresponding to equal radii and equal central angles) are equal.

Step2: Evaluate each option

• Option A: $PH=HI$ is not required for parallel construction.
• Option B: $IJ=PQ$ holds as they are congruent arcs from equal compass settings.
• Option C: $AI=IB$ is not necessary; $I$ can be any point on $\overleftrightarrow{AB}$.
• Option D: $SI=AI$ is not required for this construction.

Answer:

B. $IJ = PQ$