Line PM is equals to line RN.
How to prove equality of lines.
Given
M is the midpoint of PQ
M is the average of P and Q
M = (P + Q)/2
Similarly,
N is the midpoint of RS,
N is the average of R and S.
N = (R + S)/2
Also,
Given that PQ = RS
Equate the expressions for M and N:
(P + Q)/2 = (R + S)/2
Cross-multiply
P + Q = R + S
Subtract Q from both sides of the equation.
P = R + S - Q
add M to both sides:
P + M = R + S - Q + (P + Q)/2
Simplifying this expression
P + M = R + S
Therefore, PM is equals to RN