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ΔABC is similar to ΔFED. Answer the questions to find the length of DF .

1. Which side in ΔFED does AB in ΔABC correspond to?
Write your answer in the space below.

2. Which side in ΔFED does CB in ΔABC correspond to?

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ChoiSungHyun ChoiSungHyun · Answer 1 · 2021-01-08T12:05:53+01:00

Step-by-step explanation:

ΔABC is similar to ΔFED.

AB are the first 2 letters in ΔABC. Similarly, FE are the first 2 letters in ΔFED.

Hence side AB corresponds to side FE.

CB are the last 2 letters in ΔABC. Similarly, DE are the last 2 letters in ΔFED.

Hence side CB corresponds to side DE.

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Vickynehra Vickynehra · Answer 2 · 2022-05-10T13:08:51+02:00

Answer:

1. EF in ΔFED corresponds to AB in ΔABC.

2. DE in ΔFED corresponds to CB in ΔABC.

3. The length of DF is 10.

Step-by-step explanation:

Given: ΔABC is similar to ΔFED. Find the length of DF.

To Find: The length of side DF in ΔFED

Since, ΔFED is a right-angled triangle and also similar to ΔABC,

Applying similarity of triangles principle,

AB = 4 , EF = 8

BC = 3 , DE = 6

Now, applying Pythagorean theorem on ΔFED,

Hypotenuse² = Length² + Base²

⇒ DF² = DE² + EF²

⇒ DF² = 6² + 8²

⇒ DF² = 100

⇒ DF = √100

⇒ DF = 10

Final Answer: Hence the length of side DF is 10.