Question

step statement reason

• abcd is a parallelogram

1 (overline{bg} cong overline{dh}) (overline{ae} cong overline{fc}) given
2 (overline{ef} cong overline{ef}) reflexive property
3 (overline{af} cong overline{ce}) congruent segments added to congruent segments form congruent segments
4 (overline{ad} cong overline{bc}) opposite sides of a parallelogram / rhombus / rectangle / square are congruent
5 (overline{ah} cong overline{cg}) congruent segments subtracted from congruent segments form congruent segments
6 (overline{ad} parallel overline{bc}) opposite sides of a parallelogram / rhombus / rectangle / square are parallel
7 (angle gce cong angle haf) parallel lines cut by a transversal form congruent alternate interior angles
8 (\triangle cge cong \triangle ahf) sas
9 (overline{ge} cong overline{fh}) select a reason...
(note: there is a diagram of parallelogram abcd with points g, e, f, h on sides bc, ac, ac, ad respectively, and markings for congruent segments and parallel sides. also, note: (overline{ac}), (overline{bc}) and (overline{ad}) are segments.)

Explanation:

Step1: Recall Congruent Triangles Property

If two triangles are congruent (like $\triangle CGE \cong \triangle AHF$ by SAS), their corresponding parts (sides and angles) are congruent. This is the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem.

Step2: Apply CPCTC to $\triangle CGE$ and $\triangle AHF$

Since $\triangle CGE \cong \triangle AHF$, the corresponding sides $\overline{GE}$ and $\overline{FH}$ must be congruent. So the reason is "Corresponding Parts of Congruent Triangles are Congruent (CPCTC)".

Answer:

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)