Question

Which theorem or postulate justifies that angle HEF~angle HGE ?

A. AA similarity postulate
B. SAS similarity theorem
C. SSS similarity theorem
D. SSA similarity theorem

Answer 1

Option A is correct.

AA similarity postulate justifies that
`\triangle HEF \sim \triangle HGE`

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`

Answer 2

I think the correct answer from the choices listed above is option A. The postulate the justifies that HEF = HGE would be the AAA similarity postulate. It states that two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.