Question

use the diagram below to answer questions 1 and 2. 1. if lm = 22 and mn = 15, find ln. 2. if ln = 54 and lm = 31, find mn. 3. if rt = 36, find the value of x. 4. if df = 9x - 39, find ef. 5. if uw = 6x - 35, find uw. 6. if hj = 7x - 27, find the value of x. 7. if bd = 7x - 10, bc = 4x - 29, and cd = 5x - 9, find each value. 8. if bd = bc, bd = 5x - 26, bc = 2x + 1, and ac = 43, find ab.

Explanation:

Step1: Use segment - addition postulate

For question 1: $LN=LM + MN$, so $LN=22 + 15=37$.

Step2: Rearrange segment - addition formula

For question 2: $MN=LN - LM$, so $MN=54 - 31 = 23$.

Step3: Set up equation for $RT$

For question 3: $RT=RS+ST$, so $36=(6x + 1)+(x + 7)$, $36=7x+8$, $7x=28$, $x = 4$.

Step4: Set up equation for $DF$

For question 4: $DF=DE + EF$, so $9x-39=47+(3x + 10)$, $9x-39=3x + 57$, $6x=96$, $x = 16$, $EF=3x + 10=3\times16+10=58$.

Step5: Set up equation for $UW$

For question 5: $UW=UV+VW$, so $6x-35=19+(4x - 20)$, $6x-35=4x - 1$, $2x=34$, $x = 17$, $UW=6x-35=6\times17-35=67$.

Step6: Set up equation for $HJ$

For question 6: $HJ=HI+IJ$, so $7x-27=(3x - 5)+(x - 1)$, $7x-27=4x - 6$, $3x=21$, $x = 7$.

Step7: Set up equation for $BD$

For question 7: $BD=BC + CD$, so $7x-10=(4x - 29)+(5x - 9)$, $7x-10=9x-38$, $2x=28$, $x = 14$. Then $BC=4x-29=4\times14-29=27$, $CD=5x - 9=5\times14-9=61$, $BD=7x-10=7\times14-10=88$.

Step8: Use $BD = BC$

For question 8: Since $BD = BC$, $5x-26=2x + 1$, $3x=27$, $x = 9$. $BC=2x + 1=19$, $AB=AC - BC=43-19=24$.

Answer:

1. $LN = 37$
2. $MN = 23$
3. $x = 4$
4. $EF = 58$
5. $UW = 67$
6. $x = 7$
7. $x = 14$, $BC = 27$, $CD = 61$, $BD = 88$
8. $AB = 24$