Question

Can someone explain the 3rd step? I don't really get how that works. We were given that step in class but I did everything else
KMNP is a square and triangle XMN is equilateral. Prove that triangle KMX is congruent to triangle PNX

I did this:
KM = PN (sides of a square)
MX = NX (sides of equilateral triangle)
KMX = PNX = 30 degrees (Angle of square - Angle of equilateral triangle)
Therefore Triangle KMX is congruent to Triangle PNX (SAS)

Answer 1

is that the right visualization??

Answer 2

I'm just checking my textbook

Answer 3

I'll draw the correct one:

Answer 4

the step 3 means, say angle PNK is θ then angle MNK is α, but because it's equilateral triangle angle NMK is also α therefore XMK is also θ