Question

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 1

The triangles are similar

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

`FD^(2)=FE^(2)+DE^(2)`

substitute the given values

`FD^(2)=3^(2)+4^(2)`

`FD^(2)=25`

`FD^(2)=5\ units`

step 2

In the right triangle BUG

Find the length of side GU

Applying the Pythagoras Theorem

`BG^(2)=BU^(2)+GU^(2)`

substitute the given values

`10^(2)=6^(2)+GU^(2)`

`GU^(2)=100-36`

`GU^(2)=8\ units`

step 3

Find the ratio of its corresponding sides

If the triangles are similar

`(FD)/(BG)=(FE)/(BU)=(DE)/(GU)`

substitute the given values

`(5)/(10)=(3)/(6)=(4)/(8)`

[tex0.5=0.5=0.5[/tex] -----> is true

therefore

The triangles are similar