Answer:
The triangles are similar
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
step 1
In the right triangle FED
Find the length of side FD
Applying the Pythagoras Theorem
[tex]FD^{2}=FE^{2}+DE^{2}[/tex]
substitute the given values
[tex]FD^{2}=3^{2}+4^{2}[/tex]
[tex]FD^{2}=25[/tex]
[tex]FD^{2}=5\ units[/tex]
step 2
In the right triangle BUG
Find the length of side GU
Applying the Pythagoras Theorem
[tex]BG^{2}=BU^{2}+GU^{2}[/tex]
substitute the given values
[tex]10^{2}=6^{2}+GU^{2}[/tex]
[tex]GU^{2}=100-36[/tex]
[tex]GU^{2}=8\ units[/tex]
step 3
Find the ratio of its corresponding sides
If the triangles are similar
[tex]\frac{FD}{BG}=\frac{FE}{BU}=\frac{DE}{GU}[/tex]
substitute the given values
[tex]\frac{5}{10}=\frac{3}{6}=\frac{4}{8}[/tex]
[tex0.5=0.5=0.5[/tex] -----> is true
therefore
The triangles are similar
