Parallel and Intersecting Lines | IT

Question 6

Observe Fig. 5.5 and describe the way the line segments meet or cross each other in each case, with appropriate mathematical words (a point, an endpoint, the midpoint, meet, intersect) and the degree measure of each angle.

Solution

Understand the Question

To describe how line segments interact in a given figure, we use specific geometric terms:

Parallel lines/segments: Line segments that never meet or intersect, maintaining an equal distance throughout.
Intersecting segments: Line segments that cross each other at a single common point (point of intersection).
Meeting at an endpoint: Line segments that share a common vertex to form an angle of a given degree measure.

(i) Describe the way line segments $\text{ST}$ and $\text{UV}$ interact.

Step 1 · Observe Segments ST and UV

Diagram 1

Segments $\text{ST}$ and $\text{UV}$ are parallel to each other. They do not meet or intersect.

Answer

(i) Segments $\text{ST}$ and $\text{UV}$ are parallel and do not meet or intersect.

(ii) Describe the way line segments $\text{AB}$ and $\text{CD}$ interact.

Step 1 · Observe Segments AB and CD

Diagram 2

Segments $\text{AB}$ and $\text{CD}$ cross each other at a single point $\text{X}$ , which is their point of intersection.

Answer

(ii) Segments $\text{AB}$ and $\text{CD}$ intersect at point $\text{X}$ .

(iii) Describe the way line segments $\text{PQ}$ and $\text{OR}$ interact.

Step 1 · Observe Segments PQ and OR

Diagram 3

Segments $\text{PQ}$ and $\text{OR}$ are parallel. They do not meet or intersect.

Answer

(iii) Segments $\text{PQ}$ and $\text{OR}$ are parallel and do not meet or intersect.

(iv) Describe the way line segments $\text{FG}$ and $\text{FH}$ interact and state the angle measure.

Step 1 · Observe Angle Formed by FG and FH

Diagram 4

Segments $\text{FG}$ and $\text{FH}$ meet at a common endpoint $\text{F}$ (the vertex).

$\angle \text{FGH} = 115.3^\circ$

Answer

(iv) Segments $\text{FG}$ and $\text{FH}$ meet at point $\text{F}$ , forming an angle of $115.3^\circ$ .

(v) Describe the way line segments $\text{IL}$ and $\text{MJ}$ interact.

Step 1 · Observe Segments IL and MJ

Diagram 5

Segments $\text{IL}$ and $\text{MJ}$ cross each other at a single point $\text{Y}$ , which is their point of intersection.

Answer

(v) Segments $\text{IL}$ and $\text{MJ}$ intersect at point $\text{Y}$ .

Common Mistakes

Meeting vs. Intersecting: Confusing segments that meet at an endpoint (sharing a vertex to form an angle) with segments that cross/intersect through one another at an internal point.
Parallel Lines: Assuming non-touching segments are always parallel without verifying that they maintain an equal distance and would never meet even if extended.

Question 6

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