Given: AB = 28; M lies on the line AB
Prove: M is a midpoint.
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.
To prove that M is a midpoint, we need to show that AM = MB.
Given: AB = 28 (length of segment AB)
Step 1: Draw a line segment AB with length 28.
(This is given in the problem statement.)
Step 2: Select a point M on the line AB.
(M lies on the line AB according to the problem statement.)
Step 3: Measure the distance between point A and point M, and the distance between point M and point B.
(Use a ruler or any other measuring tool to find the lengths AM and MB.)
Step 4: Check if AM = MB.
(Compare the measured lengths of AM and MB obtained in Step 3.)
Step 5: If AM = MB, then M is a midpoint.
(If the measured lengths AM and MB are equal, then the point M divides the line segment AB into two equal parts, and M is considered as a midpoint.)
Step 6: Write the proof.
(Write a logical sequence of statements and reasons based on the steps that have been completed.)
Final proof:
Based on the given information and the steps conducted, we have measured the length of AM and MB to find that they are equal. Therefore, we can conclude that M is a midpoint of the line segment AB.