Lines and Angles

Question 1: Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the angles formed between the fold and the sides of the paper. Make different angles by folding a rectangular sheet of paper and compare the angles. Which is the largest and smallest angle you made?

Folding Paper and Comparing Angles

1. Acute Angle (Less than 90°)

   /
  /
 /____
   45°
  • This angle is small.
  • Example: 45°

2. Right Angle (90°)

 |
 |
 |____
   90°
  • This is called a right angle.
  • Example: 90°

3. Obtuse Angle (More than 90°)

   \
    \
_____\
 120°

  • This angle is wide.
  • Example: 120°

Comparison of Angles

  • Acute Angle < Right Angle < Obtuse Angle

Largest and Smallest Angle

  • Largest Angle: Obtuse Angle
  • Smallest Angle: Acute Angle
Question 2: In each case, determine which angle is greater and why.
a. \(\angle AOB\) or \(\angle XOY\)
Answer: \(\angle XOY\) is greater.
Reason: By visual inspection of the opening width between the arms, the gap between ray \(OX\) and ray \(OY\) spreads open wider than the gap between ray \(OA\) and ray \(OB\).

b. \(\angle AOB\) or \(\angle XOB\)
Answer: \(\angle XOB\) is greater.
Reason: Ray \(OX\) lies further away from ray \(OB\) than ray \(OA\) does, making the rotational opening larger.
c. \(\angle XOB\) or \(\angle XOA\)
Answer: \(\angle XOA\) is greater.
Reason: \(\angle XOA\) entirely contains \(\angle XOB\) inside its space plus the additional space of \(\angle AOB\).
Question 3: Which angle is greater: \(\angle XOY\) or \(\angle AOB\)? Give reasons.

Answer: \(\angle XOY\) is greater than \(\angle AOB\).
Reasoning by Superimposition:
  • Trace \(\angle AOB\) onto a transparent sheet of paper.
  • Place the traced vertex \(O\) directly over vertex \(O\) of \(\angle XOY\).
  • Align the base arm \(OB\) exactly on top of arm \(OY\).
You will observe that arm \(OX\) extends further out past arm \(OA\), confirming that \(\angle XOY\) has a wider spread.