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What other information do you need to prove GHK ≅ KLG by SAS?


A. ∠KHG ≅ ∠GLK
B. ∠HGK ≅ ∠LKG
C. ∠GHK ≅ ∠KLG
D. ∠HKG ≅ ∠LGK

What other information do you need to prove GHK KLG by SAS A KHG GLK B HGK LKG C GHK KLG D HKG LGK class=

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Step-by-step explanation:

We know that HK and GL are congruent by Given. We can also see that GK is congruent to itself on both sides because of reflexive property. A works, because it corresponds and might fit into SAS. B doesn't, because the two angles don't correspond. C is the same as A, so it will work as well. D's angles correspond, but don't fit SAS.

This means that angle KHG and angle GLK will be congruent, as well as angles GHK and KLG (They're the same angles though).

akposevictor

To prove that [tex]\triangle GHK \cong \triangle KLG[/tex] by the SAS Congruence Theorem, the additional information we need is: D. ∠HKG ≅ ∠LGK

Recall:

  • If two sides and an included angle in one triangle is congruent to two sides and an included angle in another triangle, both triangles are proven by the SAS Congruence Theorem to be congruent to each other.

Given the image showing [tex]\triangle GHK $ and $ \triangle KLG[/tex], the following are known:

[tex]HK \cong GL\\\\GK \cong GK[/tex]

  • This implies that two corresponding sides of both triangles are congruent to each other.

However, for us to prove that both triangles to be congruent, we need an additional information that tells us an included angle in one triangle is congruent to a corresponding included angle in the other.

Therefore, to prove that [tex]\triangle GHK \cong \triangle KLG[/tex] by the SAS Congruence Theorem, the additional information we need is: D. ∠HKG ≅ ∠LGK

Learn more here:

https://brainly.com/question/16986516

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