Question

1. Line SD is a line of symmetry for figure AXPDZHMS. Noah says that AXPDS is congruent to HMZDS because sides AX and HM are corresponding.
Part a: Why is Noah's congruence statement incorrect?

Part b: Write a correct congruence statement for the pentagons.​

Answer 1

Answer/Step-by-step explanation:

Part A:

If a figure is divided into two equal halves by a line of symmetry, each of the pair the corresponding parts will be congruent to the other part.

Thus, based on the Symmetric Figures Theorem, the two parts in the question above are congruent as a result of the line of symmetry, line SD, which makes one part the mirror image of the other.

Therefore, Noah's congruence statement is of the pentagons is incorrect.

Part B:

Based on Symmetric Figures Theorem, AXPDS is congruent to MHZDS as the line of symmetry, line SD, makes one a mirror image of the other.