Question

5 given: $overline{df} parallel overline{hg}$, $f$ is the midpoint of $overline{eg}$
$overline{df} cong overline{hg}$
prove: $\triangle def cong \triangle hfg$

statements	reasons
2. $f$ is the midpoint of $eg$	2.
3.	3. given
4.	4. corresponding angles
5. $overline{ef} cong overline{fg}$	5.
6. $\triangle def cong \triangle hfg$	6.

Explanation:

Step1: State given parallel segments

$\overline{DF} \parallel \overline{HG}$

Step2: Cite midpoint given reason

Given

Step3: State given congruent segments

$\overline{DF} \cong \overline{HG}$

Step4: Identify congruent angles

$\angle E \cong \angle HGF$

Step5: Cite midpoint segment congruence

Definition of midpoint

Step6: Cite congruence theorem

ASA Congruence Postulate

Answer:

Statements	Reasons
2. $F$ is the midpoint of $\overline{EG}$	2. Given
3. $\overline{DF} \cong \overline{HG}$	3. Given
4. $\angle E \cong \angle HGF$	4. Corresponding Angles
5. $\overline{EF} \cong \overline{FG}$	5. Definition of midpoint
6. $\Delta DEF \cong \Delta HFG$	6. ASA Congruence Postulate