Jade constructed ∠cBa and then constructed a copy of ∠cBa and labeled it as ∠fEd. What must be true about the two angles she constructed? which is the true correct answer solve it and tell me why

Question

(1 point)
Responses

∠fEd was made by drawing two rays from point E the same length as aB¯¯¯¯¯¯¯.
angle f upper E d was made by drawing two rays from point upper E the same length as Modifying above a upper B with bar .

The copy of the angle was constructed using only a straightedge.
The copy of the angle was constructed using only a straightedge.

The angles have congruent measurements.
The angles have congruent measurements.

∠fEd has twice the measure of ∠aBc.
angle f upper E d has twice the measure of angle a upper B c .

Answer 1

The correct response is:

The angles have congruent measurements.

Explanation:

When Jade constructed a copy of the angle ∠cBa and labeled it as ∠fEd, she followed the geometric principles of angle construction. The process of copying an angle involves drawing the angle with the same measurements and opening as the original. Therefore, by definition:

• Congruent Angles: Two angles are said to be congruent if they have the same angle measurement. Since ∠fEd was constructed as a copy of ∠cBa, it follows that:

∠fEd ≅ ∠cBa.

The other options explained:

1. "∠fEd was made by drawing two rays from point E the same length as aB̄."

   • This statement may refer to construction methods but does not directly express the relationship between the two angles. Angle copy construction focuses on the measures, not specifically the lengths of the rays.

2. "The copy of the angle was constructed using only a straightedge."

   • This is inaccurate, as angle copying typically requires both a compass and a straightedge. Using just a straightedge would not allow for the accurate replication of an angle’s measurement.

3. "∠fEd has twice the measure of ∠cBa."

   • This statement is incorrect. Since ∠fEd is a copy of ∠cBa, there is no basis for one angle having twice the measure of the other; they are congruent, not proportionally different.

In summary, the angles ∠cBa and ∠fEd have congruent measurements because one is an exact copy of the other.