Question

Triangle ABC undergoes a series of transformations to result in triangle DEF.

Is triangle DEF congruent to triangle ABC ?

Is it Congruent or Not congruent?


1.)) Triangle ABC is translated 3 units up and 5 units right, and then dilated by a scale factor of 4 to form triangle DEF.
(congruent or NOT congruent)

2.)) Triangle ABC is reflected over the x-axis, and then translated 6 units down and 6 units left to form triangle DEF.
(congruent or NOT congruent)


3.)) Triangle ABC is rotated 180°, and then reflected over the line y=x to form triangle DEF.
(congruent or NOT congruent)


I personally think the first 2 are congruent, and the 3rd is not, but I am not completely sure.

Answer 1

Congruent means same size same shape...
Is 1) still the same SIZE when you do a dilation of scale factor 4...

Answer 2

I don't think it stays the same size.

Answer 3

I'm not sure about these, they are kind of hard for me to understand. But I think the size wouldn't stay the same.

Answer 4

So #1 is NOT congruent : )

Answer 5

#2 is correct : )
#3... the shape is changed if a dilation is done. A slide, flip or turn does not change the shape (just the orientation of the object).
So what do you think about 3?

Answer 6

Thanks! :)

And yes for 3, I think it's congruent. If the shape stays the same and does not change.

Answer 7

Excellent work : )

Answer 8

Thanks @MsPi_3.14159265 ! :D

I greatly appreicte your help today!! :)