Answer:
Option A is correct.
AA similarity postulate justifies that \(\triangle HEF \sim \triangle HGE\)
Step-by-step explanation:
The sum of the measures of a angles in a triangle add up to 180 degree.
In the triangle HGE:
\(\angle EHG+\angle EGH+\angle GEH = 180^{\circ}\)
Substitute the given values;
\(90^{\circ}+37^{\circ}+\angle GEH = 180^{\circ}\)
\(127^{\circ}+\angle GEH = 180^{\circ}\)
Simplify:
\(\angle GEH = 180 -127 = 53^{\circ}\)
In triangle HEF and triangle HGE
\(\angle FHE = \angle GHE = 90^{\circ}\) [Angle]
\(\angle EFH = \angle GEH = 53^{\circ}\) [Angle]
AA (Angle-Angle) similarity postulates states that two triangle are similar if they have two corresponding angles that are congruent or equal.
by AA similarity postulates;
\(\triangle HEF \sim \triangle HGE\)
