Given: AB = 28; M lies on the line AB

Question

Prove: M is a midpoint.

Answer 1

To prove that M is a midpoint, we need to show that AM = MB.

Since M lies on line AB, we can write AB as the sum of AM and MB: AB = AM + MB.

Given that AB = 28, we can substitute this into the equation: 28 = AM + MB.

Since we want to prove that M is a midpoint, we assume it is true and can therefore substitute AM and MB with x (the length of AM or MB): 28 = x + x.

Simplifying the equation, we have: 28 = 2x.

Now, solve for x by dividing both sides of the equation by 2: 14 = x.

Therefore, AM = MB = 14.

Since AM is equal to MB, we can conclude that M is the midpoint of AB.