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3 years ago

(In picture) “Explain how you know you know using proportional lengths”

Mathematics

1 answer:

gregori [183]3 years ago

7 0

9514 1404 393

Answer:

yes

Step-by-step explanation:

If GH║FE, then ∆DEF ~ ∆DHG.

In similar triangles, corresponding sides have the same ratios.

The ratios of corresponding sides are ...

DG/DF = DH/DE

DG/(DG + GF) = 18/(18+36)

(1/2GF)/((1/2GF +GF) = 1/3

(1/2)/(3/2) = 1/3

1/3 = 1/3

Corresponding sides are proportional. Angle D is congruent to itself, so ∆DEF ~ ∆DHG by the SAS similarity postulate. Angles DGH and DFE are therefore congruent and GH║FE.

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