How do I prove this shape has 2 right angles?

Question

Answer 1

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LM has a slope of 3/2

KL has a slope of -2/3

MN has a slope of -2/3

m(LM) * m(KL)

(3/2) * (-2/3) = -1.

m(LM) * m(MN)

(3/2) * (-2/3) = -1

If the products of the slopes of 2 lines is -1, then the lines are perpendicular.

Answer 2

for angle M, get lengths of MN, ML, NL and see if Pyth. theorem applies

MN² = 3² + 2² = 13

LM² = 3² + 2² = 13

NL² = 5² + 1² = 26

YES, 13+13=26

same for L

LM² = 3² + 2² = 13

LK² = 6² + 4² = 52

KM² = 4² + 7² = 65

YES

distance between two pointsd = √(Δx² + Δy² )

or

d² = Δx² + Δy²