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. a. why is noahs congruence statement incorrect? b. write a correct congruence statement for the pentagons.

Explanation:

a. For two polygons to be congruent, all corresponding sides and all corresponding angles must be equal. Noah only mentioned one - pair of corresponding sides. Just having one pair of corresponding sides equal is not enough to prove congruence.
b. Since line SD is a line of symmetry for figure AXPDZHMS, the corresponding vertices and sides on either side of the line of symmetry are equal. The correct congruence statement for the pentagons is AXPDZ $\cong$ HMZDS as the vertices are in the correct corresponding order.

Answer:

a. Noah only considered one - pair of corresponding sides; all corresponding sides and angles must be equal for congruence.
b. AXPDZ $\cong$ HMZDS