Chapter 4.5, Problem 4CYU

To determine

To prove:

  $\Delta HJF\cong \Delta FGH$ by two-column.

Explanation of Solution

Given Information:

  $\begin{array}{l}\overline{GH}\parallel \overline{FJ}\\ m\angle G=m\angle J=90°\end{array}$ .

  

Proof:

The two-column proof can be given as:

Proof	Reason
$\begin{array}{l}\overline{GH}\parallel \overline{FJ}\\ m\angle G=m\angle J=90°\end{array}$	Given.
$\angle G\cong \angle J$	Definition of congruent angles.
$\angle GHF\cong \angle JFH$	Alternate interior angles are congruent.
$\overline{HF}\cong \overline{FH}$	Reflexive property.
$\Delta HJF\cong \Delta FGH$	AAS − Angle, Angle, Side.