in this video we're going to finish the segments
addition postulate worksheet on the CUDA software website this is a free worksheet that they
provide and it's under the geometry section so our directions for numbers 15 through 18 are
to find the lengths indicated and number 15 our indicated length is C E and you can see that
they tell us that C e is x plus 26 in order to solve for C we need to figure out what that
X is because then all we have to do is add 26 to get the total length of C e you'll you
can see that B to C plus C to e will give you the total length of the segment B e and we're
given both of these so BC plus c e equals b e however we're also given b d and d e BD to de
also equals b e so since BC plus c e equals b e and BD plus de also equals b e then we can
say that b c plus C e equals BD plus de so let's go ahead and plug each of these in BC is
3x plus 47 and we're adding that to seee which is X plus 26 and that is equal to BD which is
27 plus X plus de which is 10 so there's only one variable in this entire equation so we're
going to solve for that X let's combine like terms on the left and like terms on the right 3x
plus X will be 4x and then we're adding that 247 plus 26 which will be 73 and that's equal to 27
plus 10 which is 37 and then we're adding X next I'll subtract an X from both sides continuing
my work up here we'll get that 4x minus X is 3x and we're adding 73 and that's equal to 37 my
next step will be to subtract 73 from both sides 37 minus 70 3 equals negative 36 and that's
equal to 3x next we'll divide both sides by 3 to get that X is equal to negative 12 now that
we know the value of x will be able to plug that in in order to find the length of C e we know
that x plus 26 equals segment C e and we just solve for X that value was negative 12 so we'll
plug negative 12 in for X add that to 26 and get our total length of segment C e negative 12 plus
26 gives us a positive 14 so 14 is the solution and number 15 let's move on to number 16 number
16 we're going to find B D and BD is 2x minus 4 we're given the total length of B e which is
3 X minus 1 and we know that that 3x minus 1 B e is going to be equal to C e plus BC so let's go
ahead and solve for BC so BC plus C e which is 2x minus 3 equals B e which is 3 X minus 1 so I'll
write b c + c e equals b e now I want to solve for this entire segment BC I'm going to do that by
subtracting 2x and adding 3 so I'm going to start track 2x and I'm going to add 3 to both sides so
BC is going to be equal to 3x minus 2x which is X and then negative 1 since we're subtracting that
1 plus 3 will be a positive 2 so BC equals x plus 2 we can see that BC plus CD equals BD since C
is between B and D BC we solved for and that's X plus 2 and then we're adding CD which is 2 to
get BD which is 2x minus 4 combining like terms X plus 2 plus 2 will be X plus 4 and that's equal
to 2x minus 4 so I'm going to subtract X from both sides and I'll also add 4 to both sides so that
my X is on my left cancel out and my 4 on my right cancels out 4 plus 4 is 8 so I'll get that 8 is
equal to 2x minus X which is X so now that I know the value of x I can plug that in for the X in my
expression that's equal to BD so BD is equal to 2x minus 4 and we solved that X was equal to 8 so
segment BD is equal to 2 times 8 minus 4 BD equal two times 8 which is 16 minus 4 and 16 minus 4
equals 12 so the solution and number 16 is 12 and number 17 we're finding de de is given to us
as 3 X minus 28 we can see that de plus e F plus FG is going to give us D G which is 33 so 3 X
minus 28 plus 3 X minus 30 plus X is going to equal 33 let's combine like terms on the Left 3 X
plus 3 X plus X is going to be 7 X then I'm going to combine my negative 28 since I'm subtracting
28 with my negative 30 since I'm also subtracting 30 to get a negative 58 since negative 28 plus
negative 30 is negative 58 and that is all equal to 33 I'll add 58 to both sides to get that 7x is
equal to 91 if I divide both sides by 7 I get that X is equal to 13 so now that I know what X is I
can plug that in for my X and my de expression so I'll have de equals 3x minus 28 and I know that
X is 13 so the length of segment de equals 3 times 13 minus 28 so de equals 3 times 13 is 39 and when
you subtract 28 we get a positive 11 so 11 is my solution in number 17 and number 18 I'm finding e
G and E G is given as X plus 23 we can see that e to F so segment EF plus segment F H which is 12
equals the total length 26 plus X so EF plus 12 equals 26 plus X if I subtract 12 from both sides
I'll get that e F is equal to 14 plus X so e F is 14 plus X now I can see that EF + FG equals e G
which is what we're trying to solve for so I've 14 plus X plus 14 plus X and that's equal to X
plus 23 so let's simplify 14 plus 14 is 28 and X plus X is 2x and I have X plus 23 on my right-hand
side of the equation if you're confused this is e F plus F G and that's equal to e G since F falls
between E and G and they're on the same line next I'm going to tract X from both sides when I do
that my X is on my right will cancel out and I want the X by itself so I'll go ahead and subtract
28 from the left and what I do to the left I have to do the right so 28 will cancel out so 2x
minus x equals x 23 minus 28 equals a negative 5 so X is equal to negative 5 but remember I'm
trying to find e G I know that eg is X plus 23 solved for X already I got that the value of X
is equal to negative five so segment eg equals negative 5 plus 23 so eg is equal to 18 so 18
is my solution and number 18 19 and 20 are both critical thinking questions a number 19 it says
points a B C D and E are all collinear and in that order we have our line we have a b c d and e we're
finding a c so we're trying to find a C if a e equals x plus 50 so the total length 8 e is X plus
50 and C to e is X plus 32 so in order to solve this problem it helps to draw out the picture so
based on our segment addition positive we can say that a to C plus C to e equals a e and then we'll
plug them in AC is our unknown we're adding C e which is X plus 32 and that's equal to AE which
is X plus 50 all we have to do is subtract X plus 32 so when I subtract X plus 32 I'm subtracting X
and I'm also subtracting 32 and I have to do that to both sides so I'll have that AC is equal to
X minus X which is 0 plus 50 minus 32 which is 18 now let's move on to number 20 number 20 says
to write a segment edition problem using three points like that in question 11 they asked the
student to solve for X but has a solution of x equals 20 so going back to number 11 you can see
that a B and C are collinear B is between a and C so a B plus B C equals AC and we just need them to
find X so we're gonna give them something for AC something for a B and then something for BC so a
B plus BC equals AC where X is equal to 20 so we can say that a B let's make that equal to 50 will
say that BC is equal to X and our total length AC is equal to well we know that X is 20 so 50 plus
20 equals 70 so AC is 70 and when we subtract 50 we'll get that X is 20 so this is one example of
segments a B BC and AC and their values that you can apply like in question 11 where the solution
is x equals 20 and that wraps up this geometry worksheet please remember to subscribe to my
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