Question

1. line sd is a line of symmetry for figure asmhzdpx. tyler says that asdpx is congruent to smdzh because sides as and ms are corresponding.

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

Explanation:

Part a

Step1: Analyze congruence statement rules

Congruent polygons must have corresponding vertices in order. Tyler's statement \(ASDPX\cong SMDZH\) does not follow the order of corresponding vertices based on the line of symmetry \(SD\).

Part b

Step1: Determine correct vertex order

Since \(SD\) is the line of symmetry, vertex \(A\) corresponds to \(M\), \(S\) corresponds to \(S\), \(D\) corresponds to \(D\), \(P\) corresponds to \(Z\), \(X\) corresponds to \(H\).

Answer:

a. Tyler's congruence statement is incorrect because he did not match the vertices in the correct order based on the line of symmetry. Corresponding vertices of congruent polygons (due to symmetry) should be in an order that reflects the symmetry. In this case, the order of vertices in the congruence statement should follow the reflection over line \(SD\).
b. A correct congruence statement is \(ASDPX\cong MSDZH\)