Question

In the figure below, segment CD is parallel to segment EF and point H bisects segment DE :

Answer 1

Answer:

See explanation

Step-by-step explanation:

In the figure below, segment CD is parallel to segment EF, DE is a transversal, then angles DIH and HGI are congruent as alternate interior angles when two parallel lines are cut by a transversal.

Consider triangles DIH and EGH. In these triangles,

• $\angle DIH\cong \angle EGH$ as alternate interior angles;
• $\angle DHI\cong \angle GHE$ as vertical angles;
• $DH\cong HE$ because point H bisects segment DE (given).

Thus,

$\triangle DIH\cong \triangle EGH$ by AAS postulate