If B is the midpoint of segment AC and C is the midpoint of segment AD, what is AD if CD = 9. I think AD = 18, but not sure.
correct
To find the length of AD, we can use the fact that B is the midpoint of segment AC and C is the midpoint of segment AD.
Since B is the midpoint of AC, we can conclude that AB = BC.
Similarly, since C is the midpoint of AD, we can conclude that AC = CD.
Given that CD = 9, we can substitute it into the equation AC = CD:
AC = 9.
Since AB = BC, we can substitute it into the equation AC = AB + BC:
9 = AB + AB.
Simplifying this equation, we can combine like terms:
9 = 2AB.
To isolate AB, we divide both sides of the equation by 2:
9/2 = AB.
So AB = 4.5.
Now we can find the length of AD by adding AB and BC:
AD = AB + BC = 4.5 + 4.5 = 9.
Therefore, AD = 9.
To find AD given that B is the midpoint of segment AC and C is the midpoint of segment AD, we can use the concept of segment midpoints and ratios.
Since B is the midpoint of segment AC, we know that AB is equal to BC. Similarly, since C is the midpoint of segment AD, we know that CD is equal to DA.
Given that CD = 9, we can conclude that DA = 9 as well.
To find AD, we can add the lengths of CD and DA:
AD = CD + DA
AD = 9 + 9
AD = 18
Hence, your assertion that AD = 18 is correct.