Answer:
The triangles are congruent.
Explanations:
The formula for calculating the distance between two points is expressed as
D = √(x₁ - x₂)²+(y₁ - y₂)²
For the first triangle with coordinates A(0, 0), B(3, 0), and C(0, 4).
Find the measure of the sides:
AB = √(3- 0)²
AB = √9
AB = 3
BC = √(4)²+(-3)²
BC = √25
BC = 5
AC = √(4- 0)²
AC = 4
For the other three coordinates (second triangles)
The second triangle has coordinates D(2, -1), E(2, 3), and F(-1, -1).
DE = √(3+1)²+(2-2)²
DE = √16
DE = 4
EF = √(-1-3)²+(-1-2)²
EF = √(-4)²+(-3)²
EF = √25
EF = 5
DF = √(-1-2)²+(-1+1)²
DF = √(-3)²
DF = 3
Note that for the first triangle to be congruent to the second triangle, the measure of their hypotenuse sides must be equal.
Since they are both right angled triangle and the measure of their hypotenuse (longest side) is equal that is BC = EF, hence the triangles are congruent.