Question

Two different students the next two problems show the attempts of two different students to provide a proof of the same statement. Each proof has something about it that is not quite correct. Explain how you would improve the argument. Given: Lines n and m intersect at point p. Prove: Angle 1 is congruent to angle 3?

Answer 1

To prove that Angle 1 is congruent to Angle 3, we can use the fact that opposite angles are congruent, and angles congruent to the same angle are congruent to each other.

Step-by-step explanation:

To prove that Angle 1 is congruent to Angle 3, we need to show that they have the same measure.

One way to improve the argument is to use the fact that when two lines intersect, opposite angles are congruent. Since Line n and Line m intersect at point p, we can conclude that Angle 2 is congruent to Angle 4, as they are opposite angles.

Next, we can use the fact that if two angles are congruent to a third angle, then they are congruent to each other. Since we know that Angle 2 is congruent to Angle 4, and Angle 2 is also congruent to Angle 1 (given in the problem), we can conclude that Angle 1 is congruent to Angle 4. And since Angle 4 is congruent to Angle 3 (opposite angles), we can conclude that Angle 1 is congruent to Angle 3.