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
$d= \sqrt{(x2-x1)^2 + (y2-y1)^2}$

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

The length of WY = $\sqrt{(4-1)^2 + (5-8)^2}$ = 3√2
The length of WX = $\sqrt{(7-1)^2 + (8-8)^2}$ = 6
The length of WZ = $\sqrt{(1-1)^2 + (2-8)^2}$ = 6
The length of XY = $\sqrt{(4-7)^2 + (5-8)^2}$ = 3√2
The length of ZY = $\sqrt{(1-4)^2 + (2-5)^2}$ = 3√2

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

∴ ΔWYZ is congruent to ΔWYX by SSS method