Question

(10th grade GEOMETRY help)

To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that DE/GF=EF/HF and


∠DFE is 4 times greater than ∠GFH.

∠FHG is the measure of ∠FED.

∠DFE is congruent to ∠GFH.

∠FHG is congruent to ∠EFD.

Answer 1

to SAS similarity both corresponding sides and angle between them should be same or similar

am confused little bit in DE/GF=EF/HF in ur question
should be DF/GF=EF/HF..
so (with my assumption) ∠GFH=∠DFE

Answer 2

Option C is correct.

`\angle DFE` is congruent to
`\angle GFH`

Explanation:

Given:

DG = 12 units, GF = 4 units , EH = 9 units and HF = 3 units

then;

DF = DG +GF = 12+4 = 16 and EF = EH+HF = 9+3 =12

In ΔDFE and ΔGFH

`(GF)/(DF) = (4)/(16) =(1)/(4)`

`(HF)/(EF) = (3)/(12) =(1)/(4)`

therefore;

`(GF)/(DF)=(HF)/(EF)`

`\angle DFE \cong \angle GFH` [angle]

By SAS(Side-Angle-Side) Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Therefore, by SAS Similarity theorem;

△DFE
`\sim`△GFH

Therefore, the only condition is
`\angle DFE` is congruent to
`\angle GFH`