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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

Which theorem or postulate justifies that angle HEFangle HGE A AA similarity postulate B SAS similarity theorem C SSS similarity theorem D SSA similarity theore class=

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MissPhiladelphia
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.

Answer:

Option A is correct.

AA similarity postulate justifies that [tex]\triangle HEF \sim \triangle HGE[/tex]

Step-by-step explanation:

The sum of the measures of a angles in a triangle add up to 180 degree.

In the triangle HGE:

[tex]\angle EHG+\angle EGH+\angle GEH = 180^{\circ}[/tex]

Substitute the given values;

[tex]90^{\circ}+37^{\circ}+\angle GEH = 180^{\circ}[/tex]

[tex]127^{\circ}+\angle GEH = 180^{\circ}[/tex]

Simplify:

[tex]\angle GEH = 180 -127 = 53^{\circ}[/tex]

In triangle HEF and triangle HGE

[tex]\angle FHE = \angle GHE = 90^{\circ}[/tex]   [Angle]

[tex]\angle EFH = \angle GEH = 53^{\circ}[/tex]  [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;

[tex]\triangle HEF \sim \triangle HGE[/tex]

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