100 POINTS // WILL AWARD PLEASE ANSWER
Use rigid motions to explain whether the triangles in the figure are congruent. Be sure to describe specific rigid motions in your explanation

The answer and explanation is in the image.

See image

Step-by-step explanation:

See image. You can use rigid motions, which don't stretch the shape. The possible rigid motions are reflection (flip) and translations (slide)

Obviously there's more than one way to slide triangle ABC onto triangle EDF.

See image. You could reflect the triangle over the y-axis. Then translate the shape left 2 units and down 4 units. Then triangle ABC will slide right exactly onto triangle EDF showing that they are congruent.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

for certain loans like mortgage loans, lenders scrutinize your debt to income ratio when you are applying for credit because it them evaluate your ability to repay your debts.