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


Prove ΔDIH ≅ ΔEGH.

In the figure below, segment CD is parallel to segment EF and point H bisects segment DE :Prove ΔDIH ≅ ΔEGH. class=

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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,

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

Thus,

[tex]\triangle DIH\cong \triangle EGH[/tex] by AAS postulate

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