Question

use a ruler to measure the length of the segment to the nearest half - inch.

1. n————m
2. x————y

sketch the three collinear points. then write the segment addition postulate for the points.

1. j is between l and m.
2. y is between w and x.

use the diagram at the right to complete the statement.

1. the point between c and f is?
2. the point between? and g is d.
3. the point between b and? is h.
4. the point between b and a is?
5. the point between? and d is g.
6. the point between a and? is d.

find the length.

1. find ac. a 6 b 12 c
2. find mn. m——14——n 8 o
3. find xz. x 134 y 61 z
4. find qr. q——18.4——r 14.2 s

plot the points in a coordinate plane. then draw segments ab, cd, ef, and gh. determine which pair of segments are congruent.

1. a(-3, 3), b(3, 3), c(-3, 1), d(2, 1), e(4, 2), f(4, -4), g(-1, 0), h(-1, -4)
2. a(-4, 2), b(-4, -2), c(-1, 3), d(-1, -3), e(2, 3), f(2, -2), g(-3, -3), h(3, -3)
3. write an expression for ac. a 2x - 3 b x + 1 c
4. write an expression for fg. f——5x——g 3x - 2 h
5. the height of the tree shown at the right is 32 feet. you climb the tree and cut a section off the top at the point shown. how tall is the part of the tree you cut off? 32 feet cut 25.5 feet

Explanation:

Step1: Solve problem 11

To find $AC$, we add the lengths of $AB$ and $BC$. Given $AB = 6$ and $BC=12$.
$AC=AB + BC=6 + 12$

Step2: Calculate the sum

$6+12 = 18$

Step3: Solve problem 12

To find $MN$, we know that $MO=14$ and $NO = 8$. Using the segment - addition relationship $MO=MN+NO$, so $MN=MO - NO$.
$MN=14 - 8$

Step4: Calculate the difference

$14 - 8=6$

Step5: Solve problem 13

To find $XZ$, we add the lengths of $XY$ and $YZ$. Given $XY = 134$ and $YZ = 61$.
$XZ=XY+YZ=134 + 61$

Step6: Calculate the sum

$134+61 = 195$

Step7: Solve problem 14

To find $QR$, we know that $QS=18.4$ and $RS = 14.2$. Using the segment - addition relationship $QS=QR+RS$, so $QR=QS - RS$.
$QR=18.4-14.2$

Step8: Calculate the difference

$18.4 - 14.2 = 4.2$

Step9: Solve problem 17

To find an expression for $AC$, we add the lengths of $AB$ and $BC$. Given $AB = 2x-3$ and $BC=x + 1$.
$AC=AB+BC=(2x - 3)+(x + 1)$

Step10: Simplify the expression

$(2x-3)+(x + 1)=2x-3+x + 1=3x-2$

Step11: Solve problem 18

To find an expression for $FG$, we know that $FH = 5x$ and $GH=3x - 2$. Using the segment - addition relationship $FH=FG+GH$, so $FG=FH - GH$.
$FG=5x-(3x - 2)$

Step12: Simplify the expression

$5x-(3x - 2)=5x-3x + 2=2x+2$

Step13: Solve problem 19

To find the height of the cut - off part of the tree, we subtract the remaining height of the tree from the original height. The original height is 32 feet and the remaining height is 25.5 feet.
Height of cut - off part$=32-25.5$

Step14: Calculate the difference

$32-25.5 = 6.5$ feet

Answer:

1. $AC = 18$
2. $MN=6$
3. $XZ = 195$
4. $QR = 4.2$
5. $AC=3x - 2$
6. $FG=2x + 2$
7. 6.5 feet