Here are the step-by-step solutions for each problem on the worksheet. The main rule we are using is the
Segment Addition Postulate, which basically says: if you have a long line segment made of smaller pieces, the length of the whole thing is just the sum of the lengths of the pieces.
1) Find HF
* We know the total length $HF = 10$.
* We know one part $GF = 1$.
* To find the missing part $HG$ (marked with a ?), we subtract the known part from the total.
* $10 - 1 = 9$.
2) Find ST
* We know the total length $RT = 13$.
* We know one part $RS = 1$.
* To find the missing part $ST$ (marked with a ?), we subtract the known part from the total.
* $13 - 1 = 12$.
3) Find TU
* We know the total length $TV = 32$.
* We know one part $UV = 20$.
* To find the missing part $TU$ (marked with a ?), we subtract the known part from the total.
* $32 - 20 = 12$.
4) Find DE
* We know the total length $CE = 30$.
* We know one part $CD = 14$.
* To find the missing part $DE$ (marked with a ?), we subtract the known part from the total.
* $30 - 14 = 16$.
5) Find KL
* Look at the line segment $IL$. The total length is 26.
* It is made of three parts: $IJ$, $JK$, and $KL$.
* We know $IJ = 9$ and $JK = 11$.
* First, add the known parts together: $9 + 11 = 20$.
* Now, subtract that sum from the total length to find $KL$: $26 - 20 = 6$.
6) Find HJ
* Look at the line segment $GJ$. The total length is not given directly, but we can figure out the pieces.
* Actually, let's look closer. The bracket for "7" covers segments $GH$ and $HI$. So, $GH + HI = 7$.
* We know $GH = 2$. This means $HI = 7 - 2 = 5$.
* The question asks for $HJ$. Segment $HJ$ is made of $HI$ and $IJ$.
* We found $HI = 5$. The diagram shows $IJ = 12$.
* Add them together: $5 + 12 = 17$.
7) Find EC
* We need to find the length from point $E$ to point $C$.
* The diagram gives us two big measurements:
* The total length $EB = 49$.
* The length $DB = 30$.
* First, let's find the length of the small piece on the left, $ED$. We subtract $DB$ from the total $EB$: $49 - 30 = 19$. So, $ED = 19$.
* Now we need $EC$. The segment $EC$ is made of $ED$ and $DC$.
* We know $ED = 19$. We also see in the diagram that $DC = 16$.
* Add them together: $19 + 16 = 35$.
8) Find IK
* We need to find the length from point $I$ to point $K$.
* The diagram gives us:
* The total length $IL = 49$.
* The length $JL = 31$.
* First, let's find the length of the piece on the far left, $IJ$. Subtract $JL$ from the total $IL$: $49 - 31 = 18$. So, $IJ = 18$.
* Now look at the middle section. We know the total length from $I$ to $L$ is 49. We know $JK = 12$.
* Let's find $IK$ directly. $IK$ is composed of $IJ$ and $JK$.
* We found $IJ = 18$. The diagram says $JK = 12$.
* Add them together: $18 + 12 = 30$.
9) Find AC
* Points A, B, and C are in a line. B is in the middle.
* This means $AC = AB + BC$.
* We are given $AB = 16$ and $BC = 12$.
* Add them: $16 + 12 = 28$.
10) Find AC
* Points A, B, and C are in a line. B is in the middle.
* This means $AC = AB + BC$.
* We are given $AB = 13$ and $BC = 9$.
* Add them: $13 + 9 = 22$.
Final Answer:
1) 9
2) 12
3) 12
4) 16
5) 6
6) 17
7) 35
8) 30
9) 28
10) 22
Parent Tip: Review the logic above to help your child master the concept of angle addition postulate worksheet pdf.
