Question

Anika constructed angle [ angle GCF ] congruent to [ angle BAC ]. Line AB and ray AC intersect at point A. Line AB runs up and down. Ray AC runs right to left. A circle arc centered at point A intersects line AB at point D and intersects ray AC at point E. A circle arc centered at point E intersects point D. A circle arc centered at point C intersects ray AC at point F. A circle arc centered at point F intersects the circle centered at point C at point G. A line goes through points C and G. Which of the following statements best justifies why [ angle GCF ] is congruent to [ angle BAC ]?

1) The angles are vertical angles.
2) The angles are corresponding angles.
3) The angles are alternate interior angles.
4) The angles are alternate exterior angles.

Answer 1

In this scenario, angle GCF and angle BAC are congruent because they are alternate interior angles.

Step-by-step explanation:

In this scenario, we have angle BAC and angle GCF, and we want to determine if they are congruent. From the given information, we can see that angle GCF is formed by the line through points C and G, and angle BAC is formed by the line through points A and B.

Since the line through points C and G is parallel to the line through points A and B, angle GCF and angle BAC are alternate interior angles. According to the alternate interior angles theorem, alternate interior angles formed by a transversal cutting through two parallel lines are congruent. Therefore, we can conclude that angle GCF is congruent to angle BAC.

The correct answer is: 3) The angles are alternate interior angles.