Given: hf || jk; hg ≅ jg prove: fhg ≅ kjg to prove that the triangles are congruent by asa, which statement and reason could be used as part of the proof? fgh ≅ kgj because vertical angles are congruent. jkg ≅ hfg because vertical angles are congruent. fhg ≅ jkg because right angles are congruent. hfg ≅ kjg because alternate interior angles are congruent.

answer:

statements that could be used as part of the proof are:

1. ∠fgh ≅ ∠kgj because vertical angles are congruent.

2. ∠hfg ≅ ∠kjg because alternate interior angles are congruent.

step-by-step explanation:

given:   hf || jk and hg ≅ jg.

to prove: δfhg ≅ δkjg by asa congruence criteria.

the triangles are congruent by asa property, if any two angles and the included side of the two triangles are congruent.

given: hf || jk  

from fig. we can see that,

∠fgh ≅ ∠kgj

reason: because these are vertically opposite angles and vertical angles are always congruent.

and hfg ≅ kjg

reason: because these are alternate interior angles and alternate interior angles are always congruent.

hence   δfhg ≅ δkjg by asa congruence property.

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step-by-step explanation:

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