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question 1

 

 

 Oct 11, 2018
 #1
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Angle FED and CEB are vertical angles and therefore congruent. 
Angle EDF and ECB are both right angles and there congruent.

Using the AA Similiarity Postulate, we can say that triangles FED and BEC are similar.
 

Now, we can use the idea that corresponding sides of similar triangles are proportional to find DF. 
First, we know that the sides of the square have lengths of  7 as DE = 2 and EC = 5, so DC = 7.
So, side BC = 7 as well.
Set up a proportion:
\(\frac{DE}{CE}=\frac{DF}{CB}\\ \frac{2}{5}=\frac{DF}{7}\\ \frac{14}{5}=DF\)
DF = 14/5 or 2.8

 Oct 11, 2018
 #2
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Thank you guest, also I feel that it is not AA Similarity Postulate but AA Similarity Criterion. Just my opinion about it

 Oct 11, 2018

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