Given:
[tex]\overline{HG}||\overline{JI},\overline{GI}\cong \overline{IK}[/tex] and [tex]\angle HIG\cong \angle JKI[/tex]
To prove:
[tex]\angle H\cong \angle J[/tex]
Solution:
In [tex]\Delta GHI[/tex] and [tex]\Delta IJK[/tex],
Statements Reasons
[tex]\overline{HG}||\overline{JI},\overline{GK}[/tex] is transversal. (Given)
[tex]\angle HGI\cong \angle JIK[/tex] (Corresponding angles)
[tex]\overline{GI}\cong \overline{IK}[/tex] (Given)
[tex]\angle HIG\cong \angle JKI[/tex] (Given)
Two angles and their included side are congruent in both triangles. So,
[tex]\Delta GHI\cong \Delta IJK[/tex] (ASA postulate)
[tex]\angle H\cong \angle J[/tex] (CPCTC)
Hence proved.
