Question

I need help getting the reasons and statements

Answer 1

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.