Question

In the straightedge and compass construction of the perpendicular line below, how do you know that ?

1) the angles at the intersection of the two lines can be proven to be congruent and complementary, so they meet at a right angle and the lines are perpendicular.
2) the angles at the intersection of the two lines can be proven to be congruent and supplementary, so they meet at a right angle and the lines are perpendicular.
3) the angles at the intersection of the two lines can be proven to be congruent, so they meet at a right angle and the lines are perpendicular.
4) the angles at the intersection of the two lines can be proven to be supplementary, so they meet at a right angle and the lines are perpendicular.

Answer 1

To prove that the lines are perpendicular in the straightedge and compass construction, we need to show that the angles at the intersection of the two lines are congruent and complementary, meaning they add up to 90 degrees. The correct answer is option 3) the angles at the intersection of the two lines can be proven to be congruent, so they meet at a right angle and the lines are perpendicular.

Step-by-step explanation:

To prove that the lines are perpendicular in the straightedge and compass construction, we need to show that the angles at the intersection of the two lines are congruent and complementary, meaning they add up to 90 degrees.

1. The angles at the intersection can be proven to be congruent and complementary, so they meet at a right angle and the lines are perpendicular.
2. The angles at the intersection can be proven to be congruent and supplementary, so they meet at a right angle and the lines are perpendicular.
3. The angles at the intersection can be proven to be congruent, so they meet at a right angle and the lines are perpendicular.
4. The angles at the intersection can be proven to be supplementary, so they meet at a right angle and the lines are perpendicular.

The correct answer is option 3) the angles at the intersection of the two lines can be proven to be congruent, so they meet at a right angle and the lines are perpendicular.