The distance between two points (x₁,y1),(x₂,y₂) is d
[tex]d= \sqrt{(x2-x1)^2 + (y2-y1)^2} [/tex]
For the given problem we have
W(1,8),X(7,8),Y(4,5), and Z(1,2)
The length of WY = [tex] \sqrt{(4-1)^2 + (5-8)^2} [/tex] = 3√2
The length of WX = [tex] \sqrt{(7-1)^2 + (8-8)^2} [/tex] = 6
The length of WZ = [tex] \sqrt{(1-1)^2 + (2-8)^2} [/tex] = 6
The length of XY = [tex] \sqrt{(4-7)^2 + (5-8)^2} [/tex] = 3√2
The length of ZY = [tex] \sqrt{(1-4)^2 + (2-5)^2} [/tex] = 3√2
∴ WX = WZ ⇒⇒⇒ proved
XY = ZY ⇒⇒⇒ proved
WY = WY ⇒⇒⇒ reflexive property
∴ ΔWYZ is congruent to ΔWYX by SSS method
