What is the composition of transformations mapping ∆abc to ∆a'b"c"?

the first transformation is
a. a reflection across m
b. a rotation about b
c. translation down

the second transformation is
a. a reflection across m
b. a rotation about a
c. a translation right

∆abc is ∆a'b"c".
a. greater than
b. less than
c. congruent to

  The first transformation is a. a reflection across m.

The second transformation is b. a rotation about a.

∆ABC is c. congruent to ∆A'B"C".

Step-by-step explanation:

In the given picture, we can see that ΔABC is reflected across line m to create ΔA'B'C' such that all the corresponding points in both the triangles are equidistant from the line of reflection m.

∴ First transformation: Reflection across m.

After that, there is rotation of  ΔA'B'C' about point A' about some degrees such that, every corresponding points in both the triangles are equidistant from the point of rotation A'.

∴ Second transformation : Rotation about A'.

Since reflection and rotation are rigid transformations, therefore they produce only congruent figures.

Therefore, ∆ABC ≅ ∆A'B'C'

∆A'B'C' ≅  ∆A'B"C"

By law of transitivity of congruence,

∆ABC  ≅ ∆A'B"C"

expression #3 is not equivalent. the others are.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3