For the pair of triangles below, determine whether or not the triangles are similar. If they are similar, show your reasoning in a flowchart. If they are not similar, explain how you know.

Answer:The triangles are similarStep-by-step explanation:we know thatIf two figures are similar, then the ratio of its corresponding sides is proportionalstep 1In the right triangle FEDFind the length of side FDApplying 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 2In the right triangle BUGFind the length of side GUApplying 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 3Find the ratio of its corresponding sidesIf 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 truethereforeThe triangles are similar