Given /_ DEF and /_ EGF in the diagram below, determine if the triangles are similar. If so, write a similarity statement, and state the criterion used to support your claim.12210107071.jpg

coexpennan

coexpennan

Answered question

2020-10-27

Given DEFandEGF in the diagram below, determine if the triangles are similar. If so, write a similarity statement, and state the criterion used to support your claim.
image

Answer & Explanation

Gennenzip

Gennenzip

Skilled2020-10-28Added 96 answers

Step 1 
Given:DE=5,EF=4,FD=325,FG=52,EG=258 
In two triangles, we are aware that ABC and PQR both will be similar if 
ABPQ=BCQR=CARP 
Step 2 
Similarly, in DEF and EGF 
DEEG=5(258) 
=5×825 
=85 
EFGF=4(52) 
=4×25 
=85 
DFEF=(325)4 
=85 
Step 3 
So, in DEF and EGF 
DEEG=EFGF=DFEF=85 
So, by equation(1) both triangles are similar by SSS criteria 
Hence, DEF and EGF are similar by SSS criteria.

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