Grade 6 Lines and Angles rotating Angles

 

Q1. How many right angles do the windows of your classroom contain? Do you see other right angles in your classroom?

Answer:

A rectangular window has 4 right angles.

Yes, many other objects in the classroom also have right angles, such as:

• Door
• Blackboard
• Tables
• Books
• Notebook
• Floor tiles

Q2. Join A to other grid points in the figure by a straight line to get a straight angle. What are all the different ways of doing it?

Answer:

A straight angle is 180°.

Extend the line AB in the same straight direction.

Possible points are:

← A──B──•

•──A──B →

That is,

• Extend to the right of B.
• Extend to the left of A.

Figure (b)

Answer:

Join A to any point lying on the same straight slant line passing through B.

Extend the line beyond B or beyond A.

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Q3. Join A to other grid points in the figure by a straight line to get a right angle. What are all the different ways of doing it?
Figure (a)

Hint: 

Extend the line further as shown in the figure below. To get a right angle at A, we need to draw a line through it that divides the straight angle CAB into two equal parts.

Answer:

Since AB is horizontal, the required line should be vertical.

Possible ways:

      •
      |
A────B
      |
      •

Join A vertically upward or downward to any grid point to make 90°.

Figure (b)

Answer:

Draw a line from A perpendicular to AB.

The new line should make a 90° angle with AB.

(Use the hint by extending AB first and then drawing the perpendicular.)

Hint

Extend AB to C so that

C
 \
  \
   A
    \
     \
      B

The new line should divide the straight angle into two equal angles (90° each).

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Q4. Get a slanting crease on the paper. Now, try to get another crease that is perpendicular to the slanting crease.
(a) How many right angles do you have now? Justify why they are exact right angles.

Answer:

There are 4 right angles.

When two lines are perpendicular, they form four equal angles, each measuring 90°. Therefore, all the angles are right angles.

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(b) Describe how you folded the paper so that any other person who does not know the process can simply follow your description to get the right angle.

Answer:

1. Take a sheet of paper.

2. Fold it diagonally to make a slanting crease.

3. Open the paper.

4. Fold the paper again so that the first crease exactly overlaps itself.

5. Press the fold firmly.

6. Open the paper.

The second crease is perpendicular to the first crease, forming four right angles.