Grade 6 Lines And Angles Ex 2.1

Figure It Out:

Question 1: Rihan & Sheetal’s Challenge

Rihan’s Question: How many lines pass through one point?

Answer: Countless (Infinite).
Imagine a point is the center of a star or a sun. You can draw lines through it in every single direction—up, down, sideways, and everywhere in between! ☀️

Sheetal’s Question: How many lines pass through two points?

Answer: Only one.
If you have two points, there is only one "straightest" path that connects both. It's like a tightrope between two buildings. 🧶

Question 2:
Name the line segments in Fig. 2.4. Which of the five marked points are on exactly one of the line segments? Which are on two of the line segments?

Name the line segments:

There are four "sticks" connected here:

\(\overline{AB}\), \(\overline{BC}\), \(\overline{CD}\), and \(\overline{DE}\).

The Point Challenge:

On exactly one segment: Points A and E (they are the very ends).
On two segments: Points B, C, and D (they are the "elbows" where two sticks meet).

Question 3

Name the rays shown in Fig. 2.5. Is T the starting point of each of these rays?

Part 1: Name the rays shown in Fig. 2.5

A ray is named by starting with its initial point (the source) and then any other point it passes through. There are 4 rays in this diagram:

\(\vec{TA}\)
\(\vec{TB}\)
\(\vec{TN}\)
\(\vec{TC}\)

Part 2: Is T the starting point of each of these rays?

Yes!

In the diagram, every single ray begins at Point T.
Think of Point T as a light bulb and the rays as the beams of light shooting out from it in different directions. 🔦

Question 4

Draw a rough figure and write labels appropriately to illustrate each of the following:

a. \(\vec{OP}\) and \(\vec{OQ}\) meet at O.
b. \(\overleftrightarrow{XY}\) and \(\overleftrightarrow{PQ}\) intersect at point M.
c. Line \(l\) contains points E and F but not point D.
d. Point P lies on \(\overline{AB}\).

Draw a rough figure

In this question, we have to follow the instructions to draw our own math pictures.

Question 5

In Fig. 2.6, name:

a. Five points
b. A line
c. Four rays
d. Five line segments

Looking at the diagram in your image with points A, B, C, D, E, and O:

a. Five points:

- Any five dots: A, B, C, D, E (or O).
b. A line:
- The long straight path with arrows on both ends: Line DB (or Line DE).
c. Four rays:
- Rays start at O and shoot out: \(\vec{OA}\), \(\vec{OB}\), \(\vec{OC}\), \(\vec{OD}\).
d. Five line segments:

Pieces of the lines: \(\overline{DE}\), \(\overline{EO}\), \(\overline{OB}\), \(\overline{OC}\), \(\overline{OA}\).

Question 6.

Here is a ray \(\vec{OA}\) (Fig. 2.7). It starts at O and passes through the point A. It also passes through the point B.

a. Can you also name it as \(\vec{OB}\)? Why?
b. Can we write \(\vec{OA}\) as \(\vec{AO}\)? Why or why not?

Solutions

a. Can you also name it as \(\vec{OB}\)? Why?

Answer: Yes.
Reason: A ray is named by its starting point and any other point it passes through. Since this ray starts at O and passes through B on its way to infinity, \(\vec{OB}\) describes the exact same path as \(\vec{OA}\).

b. Can we write \(\vec{OA}\) as \(\vec{AO}\)? Why or why not?

Answer: No.
Reason: In ray notation, the first letter must be the starting point. \(\vec{OA}\) starts at O and goes toward A. If we wrote \(\vec{AO}\), it would mean the ray starts at A and goes toward O, which is a different direction! 🚫