Question

what is the missing statement for step 7 in this proof?
a. △dgh ≅ △feh
b. △ghf ≅ △ehd
c. △dgf ≅ △fed
d. △def ≅ △edg
prove:

proof
1 quadrilateral defg is a parallelogram given
2 de || gf
dg || ef definition of a parallelogram
3 draw df and ge these line segments are transversals cutting two pairs of parallel lines de and gf and dg and ef drawing line segments
4 place point h where df and ge intersect defining a point
5 ∠hgd ≅ ∠hef
∠hdg ≅ ∠hfe
6 dg ≅ ef opposite sides of a parallelogram are congruent
7
8 gh ≅ eh asa criterion for congruence
dh ≅ fh corresponding sides of congruent triangles are congruent

Explanation:

Step1: Recall ASA criterion

ASA (Angle - Side - Angle) criterion for congruence of triangles states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Identify the triangles

In the proof, we have \(\angle HGD\cong\angle HEF\), \(\angle HDG\cong\angle HFE\), and \(DG\cong EF\). The triangles \(\triangle DGH\) and \(\triangle FEH\) have two angles and the included side (for \(\triangle DGH\) the side is \(DG\) and for \(\triangle FEH\) the side is \(EF\)) congruent.

Answer:

A. \(\triangle DGH\cong\triangle FEH\)