Question

I need help with this if you get it right I will mark you

Answer 1

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Answer:

  D  9/DF = 18/16

Step-by-step explanation:

Corresponding sides are proportional. The proportions based on a given similarity statement can be written 4 ways.

For these isosceles triangles, the similarity statement could be written either of two ways:

  ΔDEF ~ ΔABC  or  ΔDEF ~ ΔCBA

Corresponding sides will depend on the similarity statement you use. Using the first one, they are ...

  DF and AC (short sides)

  DE and AB (long sides)

  EF and BC (long sides)

For each (short side, long side) pair, we can write the proportion 4 ways:

• DF/DE = AC/AB  ⇒  DF/9 = 16/18
• DF/AC = DE/AB  ⇒  DF/16 = 9/18
• DE/DF = AB/AC  ⇒  9/DF = 18/16 . . . . . matches choice D
• AC/DF = AB/DE  ⇒  16/DF = 18/9

Using the other pair of long sides, or using the other similarity statement, the numerical proportions are the same as the ones listed above.