Question

parallel and perpendicular lines : shapes
part - a
write a relation between the line segments indicated by the arrows in each shape.
1)
2)
3)
4)
5)
6)
part - b
identify the pair of parallel and perpendicular line segments in each shape. name them.
7)
perpendicular line segments:
parallel line segments:
perpendicular line segments:
parallel line segments:

Explanation:

Step1: Analyze shape 3

The arrows point to $\overline{LM}$ and $\overline{MN}$. These line segments meet at a right angle, so they are perpendicular.

Step2: Analyze shape 4

The arrows point to $\overline{WV}$ and $\overline{XU}$. These are the two parallel top and bottom sides of a trapezoid, so they are parallel.

Step3: Analyze shape 5

The arrows point to $\overline{FE}$ and $\overline{EH}$. These meet at a right angle, so they are perpendicular.

Step4: Analyze shape 6

The arrows point to $\overline{UT}$ and $\overline{VS}$. These are opposite sides of a rhombus, so they are parallel.

Step5: Analyze shape 7 (perpendicular)

Identify segments meeting at 90°: $\overline{HG} \perp \overline{GF}$, $\overline{BC} \perp \overline{CD}$, $\overline{BH} \perp \overline{HG}$, $\overline{BH} \perp \overline{BC}$.

Step6: Analyze shape 7 (parallel)

Identify segments that never intersect: $\overline{HG} \parallel \overline{BC}$, $\overline{GF} \parallel \overline{CD}$, $\overline{BH} \parallel \overline{FE}$.

Step7: Analyze shape XYWZ (perpendicular)

Identify segments meeting at 90°: $\overline{XW} \perp \overline{WZ}$, $\overline{WZ} \perp \overline{ZY}$, $\overline{ZY} \perp \overline{YX}$, $\overline{YX} \perp \overline{XW}$.

Step8: Analyze shape XYWZ (parallel)

Identify opposite parallel segments: $\overline{XW} \parallel \overline{ZY}$, $\overline{YX} \parallel \overline{WZ}$.

Answer:

Part-A

1. Perpendicular
2. Parallel
3. Perpendicular
4. Parallel

Part-B

Shape 7

Perpendicular line segments:
$\overline{HG} \perp \overline{GF}$
$\overline{BC} \perp \overline{CD}$
$\overline{BH} \perp \overline{HG}$
$\overline{BH} \perp \overline{BC}$

Parallel line segments:
$\overline{HG} \parallel \overline{BC}$
$\overline{GF} \parallel \overline{CD}$
$\overline{BH} \parallel \overline{FE}$

Shape XYWZ

Perpendicular line segments:
$\overline{XW} \perp \overline{WZ}$
$\overline{WZ} \perp \overline{ZY}$
$\overline{ZY} \perp \overline{YX}$
$\overline{YX} \perp \overline{XW}$

Parallel line segments:
$\overline{XW} \parallel \overline{ZY}$
$\overline{YX} \parallel \overline{WZ}$