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Given: M is the midpoint of PQ: N is the midpoint of RS; PQ=RS Prove: PM=RN

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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

User Curt Nichols
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