Question

Delete AC and focus on the intersection of AB and BC. Keeping points B and C fixed, move point A to different locations and observe how ∠ABC changes. What must you do to increase or decrease ∠ABC? What happens if you move point A to a location directly on CB? What is ∠ABC at this location? Explain.

a) Increase ∠ABC by moving A away from the midpoint of BC.
b) Decrease ∠ABC by moving A closer to the midpoint of BC.
c) ∠ABC remains constant regardless of the position of A.
d) ∠ABC becomes undefined if A is on CB.

Answer 1

To increase or decrease ∠ABC, move point A away or closer to the midpoint of BC. If point A is on CB, ∠ABC becomes undefined.

Step-by-step explanation:

To increase ∠ABC, you need to move point A away from the midpoint of BC. This will create a larger angle between AB and BC. Conversely, to decrease ∠ABC, you need to move point A closer to the midpoint of BC. This will create a smaller angle between AB and BC.

If you move point A to a location directly on CB, ∠ABC becomes undefined. This is because the lines AB and BC would overlap, resulting in no angle between them.