Question

question 1 - 7
marie wants to draw a line perpendicular to $overline{ab}$ passing through point $p$. the figure below shows her work
she made the following claims about her work
claim i: $overline{pa}$ is congruent to $overline{pb}$
claim ii: $overline{aq}$ is congruent to $overline{bq}$
which statement about the claims is correct?
only claim i is correct.
only claim ii is correct.
both claim i and claim ii are correct.
neither claim i nor claim ii is correct.

Explanation:

Step1: Analyze Claim I

There is no information or construction steps indicating that $\overline{PA}$ and $\overline{PB}$ are congruent. Just because there is a perpendicular - line construction does not imply these two segments are equal.

Step2: Analyze Claim II

The construction of a perpendicular line from a point $P$ to $\overline{AB}$ does not guarantee that $\overline{AQ}$ and $\overline{BQ}$ are congruent. For $\overline{AQ}$ and $\overline{BQ}$ to be congruent, the perpendicular from $P$ to $\overline{AB}$ would have to be the perpendicular - bisector of $\overline{AB}$, and there is no evidence of that in the given construction.

Answer:

Neither Claim I nor Claim II is correct.