Is it possible for the same (a) line segment to have two different lengths? (b) angle to have two different measures?
(a) No (b) No
Step 1: Understand a line segment
A line segment joins two fixed points.
Write it as: \(\overline{AB}\).
The distance between A and B is fixed.
So the same \(\overline{AB}\) cannot be both 5 cm and 6 cm.
If the length changes, it is not the same segment.
Conclusion for (a): One segment ⟶ one unique length.
Step 2: Understand an angle
An angle is formed by two fixed rays with a common vertex.
Write it as: \(\angle AOB\).
The opening between the rays OA and OB is fixed.
So the same \(\angle AOB\) cannot be both \(45^\circ\) and \(50^\circ\).
If the measure changes, it is not the same angle.
Conclusion for (b): One angle ⟶ one unique measure.
Final: (a) No. (b) No.