In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3. Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3. To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and ∠DFE is 4 times greater than ∠GFH. ∠FHG is One-fourth the measure of ∠FED. ∠DFE is congruent to ∠GFH. ∠FHG is congruent to ∠EFD.

To prove that △DFE ~ △GFH by SAS similartiy theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: = and ∠DFE is congruent to ∠GFH.

Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:

By comparing ΔDEF and ΔGFH

DF = DG + GF

     = 12 + 4

DF = 16

Also,

EF = EH + HF

    = 9 + 3

EF = 12

Comparing the sides of ΔDEF and ΔGFH, we have;

=

=

4 = 4

Thus, the two triangles have similar sides.

Comparing the included angle <DFE and <GFH, then;

∠DFE is congruent to ∠GFH

So that the appropriate answer to the given question is option C. ∠DFE is congruent to ∠GFH

Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;

= and ∠DFE is congruent to ∠GFH.

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the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .