I need help getting the reasons and statements

Question

asked Jun 27, 2021 142k views

1 Answer

Menelaos Vergis · Answer 1 · 2021-07-03T06:36:24+0000

Given:

$\overline{HG}||\overline{JI},\overline{GI}\cong \overline{IK}$ and
$\angle HIG\cong \angle JKI$

To prove:

$\angle H\cong \angle J$

Solution:

In
$\Delta GHI$ and
$\Delta IJK$ ,

Statements Reasons

$\overline{HG}||\overline{JI},\overline{GK}$ is transversal. (Given)

$\angle HGI\cong \angle JIK$ (Corresponding angles)

$\overline{GI}\cong \overline{IK}$ (Given)

$\angle HIG\cong \angle JKI$ (Given)

Two angles and their included side are congruent in both triangles. So,

$\Delta GHI\cong \Delta IJK$ (ASA postulate)

$\angle H\cong \angle J$ (CPCTC)

Hence proved.