Question

complete the proof that $\angle f \cong \angle i$.

	statement	reason
1	$\overline{fg} \cong \overline{hi}$	given
2	$\overline{hi} \parallel \overline{gj}$	given
3	$\overline{fi} \parallel \overline{gh}$	given
4	$\overline{gj} \cong \overline{hi}$	parallelograms have congruent opposite sides
5	$\overline{fg} \cong \overline{gj}$	transitive property of congruence
6	$\angle fjg \cong \angle f$	isosceles triangle theorem
7	$\angle fjg \cong \angle i$	corresponding angles theorem
8	$\angle f \cong \angle i$

Explanation:

Step1: Identify the relevant property

We know from steps 6 and 7 that $\angle FJG \cong \angle F$ and $\angle FJG \cong \angle I$. To show $\angle F \cong \angle I$, we use the Transitive Property of Congruence, which states that if $a \cong b$ and $b \cong c$, then $a \cong c$. Here, let $a = \angle F$, $b = \angle FJG$, and $c = \angle I$. Since $\angle F \cong \angle FJG$ (step 6) and $\angle FJG \cong \angle I$ (step 7), by the Transitive Property of Congruence, $\angle F \cong \angle I$.

Answer:

Transitive Property of Congruence