Question

lesson 1.2
practice b continued
for use with the lesson \use segments and congruence\
in the diagram, points a, b, c, and d are collinear, points c, x, y, and z are collinear, $ab = bc = cx = yz$, $ad = 54$, $xy = 22$, and $xz = 33$. find the indicated length.

1. $ab$
2. $bd$
3. $cy$
4. $cd$
5. $xc$
6. $cz$

find the indicated length.

1. find $st$.

$\overline{rt}=32$, $\overline{rs}=4x$, $\overline{st}=12x$

1. find $ac$.

$\overline{ab}=14$, $\overline{bc}=3x-4$, $\overline{ac}=4x+4$

1. find $np$.

$\overline{mp}=6x-23$, $\overline{mn}=x-5$, $\overline{np}=3x+2$
point $j$ is between $h$ and $k$ on $\overline{hk}$. use the given information to write an equation in terms of $x$. solve the equation. then find $hj$ and $jk$.

1. $hj = 2x$

$jk = 3x$
$kh = 25$

1. $hj = \frac{x}{4}$

$jk = 3x - 4$
$kh = 22$

1. $hj = 5x - 4$

$jk = 8x - 10$
$kh = 38$

1. $hj = 5x - 3$

$jk = x - 9$
$kh = 5x$

Explanation:

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Questions 19-24

Step1: Find YZ length

$YZ = XZ - XY = 33 - 22 = 11$

Step2: Set AB = YZ

Given $AB=BC=CX=YZ$, so $AB=11$

Step3: Calculate AC length

$AC = AB + BC = 11 + 11 = 22$

Step4: Calculate CD length

$CD = AD - AC = 54 - 22 = 32$

Step5: Calculate BD length

$BD = BC + CD = 11 + 32 = 43$

Step6: Calculate CY length

$CY = CX + XY = 11 + 22 = 33$

Step7: Set XC = YZ

$XC = YZ = 11$

Step8: Calculate CZ length

$CZ = CX + XY + YZ = 11 + 22 + 11 = 44$

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Question 25

Step1: Set total length equation

$RT = RS + ST$, so $4x + 12x = 32$

Step2: Solve for x

$16x = 32 \implies x = 2$

Step3: Calculate ST length

$ST = 12x = 12 \times 2 = 24$

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Question 26

Step1: Set segment equality

$AB = 4x+4 - (3x-4) = 14$

Step2: Solve for x

$x + 8 = 14 \implies x = 6$

Step3: Calculate AC length

$AC = 4x+4 = 4\times6 +4 = 28$

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Question 27

Step1: Set segment equality

$MN = MP - NP$, so $x-5 = (6x-23)-(3x+2)$

Step2: Simplify and solve x

$x-5 = 3x-25 \implies 2x=20 \implies x=10$

Step3: Calculate NP length

$NP = 3x+2 = 3\times10 +2 = 32$

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Question 28

Step1: Set total length equation

$HJ + JK = KH$, so $2x + 3x =25$

Step2: Solve for x

$5x=25 \implies x=5$

Step3: Calculate HJ and JK

$HJ=2x=10$, $JK=3x=15$

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Question 29

Step1: Set total length equation

$\frac{x}{4} + 3x -4 =22$

Step2: Solve for x

$\frac{13x}{4}=26 \implies x=8$

Step3: Calculate HJ and JK

$HJ=\frac{8}{4}=2$, $JK=3\times8 -4=20$

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Question 30

Step1: Set total length equation

$5x-4 +8x-10=38$

Step2: Solve for x

$13x-14=38 \implies 13x=52 \implies x=4$

Step3: Calculate HJ and JK

$HJ=5\times4 -4=16$, $JK=8\times4 -10=22$

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Question 31

Step1: Set total length equation

$5x-3 +x-9=5x$

Step2: Solve for x

$6x-12=5x \implies x=12$

Step3: Calculate HJ and JK

$HJ=5\times12 -3=57$, $JK=12-9=3$

Answer:

1. $AB = 11$
2. $BD = 43$
3. $CY = 33$
4. $CD = 32$
5. $XC = 11$
6. $CZ = 44$
7. $ST = 24$
8. $AC = 28$
9. $NP = 32$
10. $HJ = 10$, $JK = 15$
11. $HJ = 2$, $JK = 20$
12. $HJ = 16$, $JK = 22$
13. $HJ = 57$, $JK = 3$