Question

Examine the two angle bisector constructions. Which angle bisector was created by following the construction steps correctly? How do you know? Which angle bisector was constructed incorrectly? Explain the step that was completed incorrectly.

a) The first construction is correct, and the second construction is incorrect due to unequal distances.
b) The second construction is correct, and the first construction is incorrect due to unequal distances.
c) Both constructions are correct.
d) Both constructions are incorrect.

Answer 1

The first construction is correct, and the second construction is incorrect due to unequal distances. Thus the correct option is A.

Step-by-step explanation:

The first construction of the angle bisector is correct while the second one is incorrect due to unequal distances. In constructing an angle bisector, the correct method involves creating two equal segments from the angle vertex to the sides of the angle, resulting in a bisector that divides the angle into two equal parts. The incorrect construction usually arises from inaccuracies in measuring or marking equal distances.

In the correct construction, the steps involve using a compass to draw arcs from the vertex of the angle to intersect both sides, creating congruent segments. The point where these segments intersect marks the angle bisector. If the distances are not equal in the second construction, it indicates an error in the process, such as inaccurate measurements or improper alignment when marking the distances.

Mathematically, for a correct angle bisector construction, the distances from the vertex to the points on the sides should be equal, ensuring that the bisector divides the angle into two congruent angles. Any discrepancy in these distances in the second construction indicates a deviation from the correct method, leading to an incorrectly constructed angle bisector. Thus the correct option is A.