Question

W(1,8),X(7,8),Y(4,5), and Z(1,2) select all methods you can use to prove WYZ is congruent to WYX

Answer 1

The distance between two points (x₁,y1),(x₂,y₂) is d

`d= √((x2-x1)^2 + (y2-y1)^2)`

For the given problem we have
W(1,8),X(7,8),Y(4,5), and Z(1,2)

The length of WY =
`√((4-1)^2 + (5-8)^2)` = 3√2
The length of WX =
`√((7-1)^2 + (8-8)^2)` = 6
The length of WZ =
`√((1-1)^2 + (2-8)^2)` = 6
The length of XY =
`√((4-7)^2 + (5-8)^2)` = 3√2
The length of ZY =
`√((1-4)^2 + (2-5)^2)` = 3√2

∴ WX = WZ ⇒⇒⇒ proved
XY = ZY ⇒⇒⇒ proved
WY = WY ⇒⇒⇒ reflexive property

∴ ΔWYZ is congruent to ΔWYX by SSS method