Are triangles △abctriangle, a, b, c and △deftriangle, d, e, f similar? to answer, try to map △abctriangle, a, b, c onto △deftriangle, d, e, f using the interactive widget.

From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .  

Step-by-step explanation:

Given as :

To Proof : Triangle Δ ABC and Triangle Δ DEF are similar

There are three methods for two Triangles to be similar

A ) SAS  i.e side angle side

B ) AA i.e angle angle

C ) SSS i.e side side side

Now,

A) If two triangle have a pair of equal corresponding angles and sides are proportional then triangle are similar

So, If in  Δ ABC and  Δ DEF

∠ B = ∠ E

and , =  

Then Δ ABC   Δ DEF

I.e SAS   similarity

B ) If two triangles have equal corresponding angles , then triangles are similar .

So, If in  Δ ABC and  Δ DEF

∠ B = ∠ E   and   ∠ A = ∠ D

Then Δ ABC   Δ DEF

I.e AA similarity

C ) If two triangles have three pairs of corresponding sides proportional then triangles are similar .

So, If in  Δ ABC and  Δ DEF

=   =

Then Δ ABC   Δ DEF

I.e SSS similarity

Hence From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .   answer