Question

1.2 measuring and constructing
name:____ date:__ period:____
segment addition
if b is between a and c, then ac = ____ + ____.
if ab + bc = ac, then ____ is ____ a and c.
segment construction
given ac = 49, find the value of x.
find the value of x.
find the length of the following segments.
if jl = 120. find jk and kl.
use your compass to copy the following segment:
use your compass to copy the following segment:

Explanation:

Step1: Segment - Addition Principle

If B is between A and C, then $AC=AB + BC$. If $AB + BC=AC$, then B is between A and C.

Step2: Solve for x when $AC = 49$

Given $AB=2x + 3$, $BC = 5x+7$ and $AC=49$. By the segment - addition postulate $AB + BC=AC$. So, $(2x + 3)+(5x + 7)=49$.
Combining like - terms: $2x+5x+3 + 7=49$, which simplifies to $7x+10 = 49$.
Subtract 10 from both sides: $7x=49 - 10=39$.
Divide both sides by 7: $x=\frac{39}{7}$.

Step3: Solve for x in the second segment problem

Given $AB = 4x-5$, $BC=11 + 2x$ and assuming $AC$ is the whole segment. By the segment - addition postulate $AB + BC=AC$. But we need more information about $AC$ to solve for $x$. Let's assume it's a valid segment addition problem and set up the equation: $(4x-5)+(11 + 2x)=AC$. Combining like - terms gives $6x + 6=AC$. If we assume $AC$ is known, we can solve for $x$. For now, if we assume it's a self - contained problem where we can set up an equation based on some unstated relationship, we can't solve it without more data.

Step4: Solve for x when $JL = 120$

Given $JK=4x + 6$, $KL=7x + 15$ and $JL = 120$. By the segment - addition postulate $JK+KL=JL$. So, $(4x + 6)+(7x + 15)=120$.
Combining like - terms: $4x+7x+6 + 15=120$, which simplifies to $11x+21 = 120$.
Subtract 21 from both sides: $11x=120 - 21 = 99$.
Divide both sides by 11: $x = 9$.

Step5: Find segment lengths

For the segment with points R, G, T, F, U, J:
We need the values on the number line to find lengths. For example, if the positions of the points on the number line are known as $R=a$, $G=b$, $T=c$, $F=d$, $U=e$, $J=f$. Then $RT=c - a$, $GT=c - b$, $UT=e - c$, $TJ=f - c$, $RF=d - a$, $JT=f - c$. But since no values are given for the positions of the points on the number line, we can't calculate the lengths.

Step6: Segment construction with compass

To copy segment PQ with a compass:

1. Place the compass point on P.
2. Open the compass to the length of PQ.
3. Without changing the compass width, place the compass point on a new starting point and draw an arc. Mark the end - point of the new segment.

To copy segment AR with a compass:

1. Place the compass point on A.
2. Open the compass to the length of AR.
3. Without changing the compass width, place the compass point on a new starting point and draw an arc. Mark the end - point of the new segment.

Answer:

1. If B is between A and C, then $AC=AB + BC$. If $AB + BC=AC$, then B is between A and C.
2. When $AC = 49$, $x=\frac{39}{7}$.
3. For the segment with $AB = 4x-5$ and $BC=11 + 2x$, more information about $AC$ is needed to solve for $x$.
4. When $JL = 120$, $x = 9$.
5. For the segment lengths with points R, G, T, F, U, J, more information (coordinates of points on number line) is needed to calculate lengths.
6. Segment construction steps are provided above for segments PQ and AR.