Joaquin drew two line segments,

Question

and

, in the
-plane. Which of the following strategies is the best for Joaquin to use to prove that the segments are congruent?

Responses

He should measure the length of both segments to the nearest inch.

Answer A: He should measure the length of both segments to the nearest inch.
A

He should perform a series of rigid transformations to show that

maps to

.

Answer B: He should perform a series of rigid transformations to show that line segment N P maps to line segment Q R .
B

He should visually observe the segments to see whether

and

appear to have the same length.

Answer C: He should visually observe the segments to see whether line segment N P and line segment Q R appear to have the same length.
C

He should find the middle of each segment and then measure to see whether each half is the same length.

Answer 1

The best strategy for Joaquin to use to prove that the segments are congruent is:

Answer B: He should perform a series of rigid transformations to show that line segment NP maps to line segment QR.

This method is the most reliable because it involves geometric transformations (such as translations, rotations, and reflections) that demonstrate the segments' congruence based on their properties, rather than just approximate measurements or visual observations. Rigid transformations preserve distance and angles, ultimately proving that the two segments are indeed congruent.