Plot point F so that △ABC ≅ △FGH. Identify a sequence of rigid motions that maps △ABC onto △FGH and use a theorem to complete the explanation of why the triangles are congruent.

Step-by-step explanation:

Point F is plotted at (5, 4)

Translate ΔABC so that point B maps to point G.

B(1, -1) → G(0, 3)  

Rule for the translation,

(x, y) → [x - 1, y + 4]

By this rule,

Point C will map the point,

C(-1, -2) → C'[(-1 - 1), (-2 + 4)]

             → C'(-2, 2)

A(-4, 0) → A'[(-4 - 1), (0 + 4)]

           → A'(-5, 4)

Now reflect these points across y-axis.

Rule for the reflection across y-axis,    

(x, y) → (-x, y)

Points after reflection will be,

A'(-5, 4) → F(5, 4)

B'(0, 3) → G(0, 3)

C'(-2, 2) → H(2, 2)

Distance formula,

d =

AB = =

BC = =

CA = =

FG =

GH =

HF =

AB ≅ FG, BC ≅ GH, CA ≅ HF          

By the SSS property Triangle congruence theorem, ΔABC ≅ ΔFGH