What does the definition of a midpoint tell you about EG and HG?
See solution
Practice makes perfect
Let's separate the two triangles and then add the given information. Note that G is the midpoint of EH which means we know that EG≅ HG according to the definition of a midpoint.
Having separated the triangles and added the given information, we can by the HL Congruence Theorem claim that the two triangles are congruent.
Alternative Solution
Two-Column Proof
Let's write this as a two-column proof.
Statement
Reason
1.
&G is the midpoint of EH
&FG≅ GI
&∠E and ∠H are right angles.
