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

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .