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In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.





To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that and
A. ∠DFE is 4 times greater than ∠GFH.
B. ∠FHG is 1/4 the measure of ∠FED.
C. ∠DFE is congruent to ∠GFH.
D. ∠FHG is congruent to ∠EFD.

In the diagram DG 12 GF 4 EH 9 and HF 3 To prove that DFE GFH by the SAS similarity theorem it can be stated that and A DFE is 4 times greater than GFH B FHG i class=

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merlynthewhizz
The diagram below shows two separate triangles, DEF and GHF

The corresponding sides FG and FD has the relationship that FD is 4 times FG

The corresponding sides FE and FH has the relationship that FE is 4 times FH

This shows the triangle DEF is 4 times length of triangle GHF

Angles in two triangles that are similar are equals.

With two sides of the same ratio and equal angles, triangle DEF and GFH are similar

The correct statement from above options is angle DFE equals to GFH

SAS similarity is side-angle-side similarity. For proving △DFE ~ △GFH, we need: Option C: ∠DFE is congruent to ∠GFH.

What is SAS similarity theorem?

ΔABC ~  ΔDEF  only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.

Suppose the two sides of ΔABC are AB and BC, and that of DEF be DE and EF, then for SAS similarity, we need

[tex]\dfrac{|AB|}{|BC|} = \dfrac{|DE|}{|EF|}[/tex] and m∠ABC = m∠DEF

where that small m means measure of that angle.

Remember that in an angle ∠ABC, we mean angle made by like AB and BC , and it is internal to the triangle ABC assuming(assumable for this context)Using the above fact to find necessary statement needed

△DFE ~ △GFH by the SAS similarity theorem,

we already have

[tex]\dfrac{|FD|}{|FE|} = \dfrac{12+4}{9+3} = \dfrac{16}{12} = \dfrac{4}{3} \\\\\\\dfrac{|FG|}{|FH|} = \dfrac{4}{3}[/tex]

Thus,

[tex]\dfrac{|FD|}{|FE|} = \dfrac{|FG|}{|FH|}[/tex]

We also have the common angle F(internal to the triangles) same(since it is common for both triangles)

Thus,

[tex]m\angle DFE = m\angle GFH\\or\\\angle DFE \cong \angle GFH[/tex]

(that middle symbol is the sign of congruency, which for angles show that their measures are same).

Thus,

The needed statement to prove △DFE ~ △GFH by the SAS similarity theorem is given as

Option C: ∠DFE is congruent to ∠GFH.

Learn more about SAS similarity theorem here: https://brainly.com/question/22472034

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