Question

practice congruent parts, part 2

1. line sd is a line of symmetry for figure axpdzhms. noah says that axpsd 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:

Step1: Recall congruence rules

For two polygons to be congruent, all corresponding sides and all corresponding angles must be equal. Just stating one - pair of corresponding sides are equal is not enough.

Step2: Identify correct corresponding parts

Since line SD is a line of symmetry, the correct corresponding vertices and sides can be identified. The correct congruence statement should have corresponding vertices in the right order.

Answer:

a. Noah's congruence statement is incorrect because for two polygons (pentagons in this case) to be congruent, all corresponding sides and all corresponding angles must be equal. Just stating that one pair of sides (AX and HM) are corresponding is not sufficient to prove congruence.
b. A correct congruence statement for the pentagons is AX PDS≅HMZDS. This is because when a figure has a line of symmetry (line SD here), the parts on either side of the line of symmetry are mirror - images of each other with all corresponding parts (sides and angles) equal.