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 e 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 n 8 o 14
3. find xz. x 134 y 61 z
4. find qr. q r 14.2 s 18.4

plot the points in a coordinate plane. then draw segments $overline{ab}$, $overline{cd}$, $overline{ef}$, and $overline{gh}$. 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: Recall segment - addition principle

For collinear points, if a point \(B\) is between points \(A\) and \(C\), then \(AC=AB + BC\).

Step2: Solve problem 11

Given \(AB = 6\) and \(BC=12\), by the segment - addition postulate \(AC=AB + BC\). Substitute the values: \(AC=6 + 12=18\).

Step3: Solve problem 12

Let \(MO = 14\) and \(NO = 8\). Since \(MO=MN+NO\), then \(MN=MO - NO\). Substitute the values: \(MN=14 - 8 = 6\).

Step4: Solve problem 13

Given \(XY = 134\) and \(YZ = 61\), by the segment - addition postulate \(XZ=XY+YZ\). Substitute the values: \(XZ=134 + 61=195\).

Step5: Solve problem 14

Let \(QS = 18.4\) and \(RS = 14.2\). Since \(QS=QR+RS\), then \(QR=QS - RS\). Substitute the values: \(QR=18.4 - 14.2 = 4.2\).

Step6: Solve problem 17

Since \(AC=AB + BC\), and \(AB = 2x-3\) and \(BC=x + 1\), then \(AC=(2x-3)+(x + 1)=2x-3+x + 1=3x-2\).

Step7: Solve problem 18

Since \(FG=FH - GH\), and \(FH = 5x\) and \(GH=3x - 2\), then \(FG=5x-(3x - 2)=5x-3x + 2=2x + 2\).

Step8: Solve problem 19

The height of the whole tree is \(32\) feet and the remaining part after cutting is \(25.5\) feet. Let the height of the cut - off part be \(h\). Then \(32=h + 25.5\), so \(h=32 - 25.5=6.5\) feet.

Answer:

1. \(18\)
2. \(6\)
3. \(195\)
4. \(4.2\)
5. \(3x - 2\)
6. \(2x + 2\)
7. \(6.5\) feet