Question

8
7
6
5
4
3
2
1
step
∠a≅∠b
△ade≅△bfg
(overline {gf}cong overline {ed})
∠adh≅∠bfh
(\begin{array}{r} square \\ square end{array} parallel \begin{array}{r} square \\ square end{array})
∠adh and ∠hdc are supplementary
∠hge≅∠hec
∠cdh≅∠cfh
(overline {dh}cong overline {fh})
(overline {gh}cong overline {eh})
statement
corresponding parts of congruent triangles are congruent (cpctc)
asa
segments
congruent segments added to congruent segments form congruent
if two angles are supplements of the same angle (or congruent angles),
then they are congruent.
select a reason...
if two angles form a linear pair, then they are supplementary
in a triangle, angles opposite of congruent sides are congruent
given
reason
c

Explanation:

Step1: Analyze the given statements and reasons

We need to find the reason for the statement in step 4. The statement in step 4 is about two angles being congruent.

Step2: Recall the relevant geometric theorems

The theorem “If two angles are supplements of the same angle (or congruent angles), then they are congruent” is relevant here.

Answer:

If two angles are supplements of the same angle (or congruent angles), then they are congruent.