Unit 3: Bisectors Worksheet Packet - LS Home Page - Free Printable

Let's solve each problem step by step based on the image you provided. The topic is bisectors, which means we're dealing with lines or segments that divide another segment into two equal parts.

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Problem 1: Mark the equal segments with tick marks

We are given three diagrams where a line segment bisects another. A bisector divides a segment into two equal parts, so we mark the equal segments with tick marks (short lines across the segments).

#### A. $\overline{AB}$ bisects $\overline{CD}$

- This means point $A$ lies on segment $\overline{CD}$, and it divides it into two equal parts.
- So, $CA = AD$
- We place one tick mark on segment $CA$ and one tick mark on segment $AD$ to show they are equal.

> ✔ Tick marks on $CA$ and $AD$

#### B. $\overline{EF}$ bisects $\overline{GH}$

- Point $F$ is on $\overline{GH}$, and since $\overline{EF}$ bisects $\overline{GH}$, it cuts $\overline{GH}$ into two equal parts at $F$.
- So, $GF = FH$
- Place one tick mark on $GF$ and one on $FH$

> ✔ Tick marks on $GF$ and $FH$

#### C. $\overline{LM}$ bisects $\overline{NP}$

- $\overline{LM}$ intersects $\overline{NP}$ at some point, say $L$, and bisects it.
- So, $NL = LP$
- Place one tick mark on $NL$ and one on $LP$

> ✔ Tick marks on $NL$ and $LP$

> 💡 Note: In all cases, the bisector passes through the midpoint of the segment being bisected.

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Problem 2: $\overline{WX}$ and $\overline{YZ}$ bisect each other

This means:
- The two segments intersect at their midpoints
- So, the intersection point (let’s call it $O$) is the midpoint of both $\overline{WX}$ and $\overline{YZ}$

So:
- $WO = OX$
- $YO = OZ$

We should mark:
- Two tick marks on $WO$ and $OX$ (to show they’re equal)
- Two tick marks on $YO$ and $OZ$ (to show they’re equal)

> ✔ Tick marks:
> - One pair on $WO$ and $OX$
> - One pair on $YO$ and $OZ$

> 💡 Since they bisect each other, the point of intersection is the midpoint of both segments.

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Problem 3: $\overline{CD}$ bisects $\overline{AB}$ at $E$, and $AB = 20$

Given:
- $\overline{CD}$ bisects $\overline{AB}$ at point $E$
- So, $E$ is the midpoint of $\overline{AB}$
- Therefore, $AE = EB$

Since $AB = 20$, then:

$$
AE = EB = \frac{20}{2} = 10
$$

#### A. $AE =$ ________

> ✔ $AE = 10$

#### B. If $AB = x + 4$, then $x = $ ________

We know $AB = 20$, so:

$$
x + 4 = 20 \\
x = 20 - 4 = 16
$$

> ✔ $x = 16$

#### C. If $EB = 4y + 2$, then $y = $ ________

We know $EB = 10$, so:

$$
4y + 2 = 10 \\
4y = 8 \\
y = 2
$$

> ✔ $y = 2$

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✔ Final Answers:

#### Problem 1:
- A: Mark $CA$ and $AD$ with one tick each
- B: Mark $GF$ and $FH$ with one tick each
- C: Mark $NL$ and $LP$ with one tick each

#### Problem 2:
- Mark $WO$ and $OX$ with one tick each
- Mark $YO$ and $OZ$ with one tick each

#### Problem 3:
- A. $AE = 10$
- B. $x = 16$
- C. $y = 2$

Let me know if you'd like a visual representation or explanation for any part!