Question

What’s the answer to this please ?

Answer 1

Yes

Explanation:

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

ΔABC:

A(2, 5), B(5, 5), C(5, 9)

`AB=√((5-2)^2+(5-5)^2)=√(3^2+0^2)=√(9+0)=\sqrt9=3\\\\AC=√((5-2)^2+(9-5)^2)=√(3^2+4^2)=√(9+16)=√(25)=5\\\\BC=√((5-5)^2+(9-5)^2)=√(0^2+4^2)=√(0+16)=√(16)=4`

ΔDEF:

D(-7, 8), E(-4, 8), F(-4, 4)

`DE=√(-4-(-7))^2+(8-8)^2)=√(3^2+0^2)=√(9+0)=\sqrt9=3\\\\DF=√((-4-(-7))^2+(4-8)^2)=√(3^2+(-4)^2)=√(9+16)=√(25)=5\\\\EF=√((-4-(-4))^2+(4-8)^2)=√(0^2+(-4)^2)=\sqrt0+16}=√(16)=4`

AB ≅ DE

AC ≅ DF

BC ≅ EF

Therefore ΔABC ≅ ΔDEF