Question

Which of the following completes the two-column proof below? HELP PLEASE!!

Given: ∠1 ≅ ∠2, p ⊥ r
Prove: q ⊥ r
Proof:
1. ∠1 ≅ ∠2 (Given)
2. p ∥ q (?)
3. p ⊥ r (?)
4. q ⊥ r (?)

Answer 1

To complete the two-column proof, statement 4 should be 'q ⊥ r' because if ∠1 ≅ ∠2 and p is perpendicular to r, then q must also be perpendicular to r.

Step-by-step explanation:

To complete the two-column proof, we need to find a statement that shows that q is perpendicular to r, just like p is perpendicular to r.

We know that ∠1 ≅ ∠2, which means that the angles formed by p and q are congruent. Since p is perpendicular to r, ∠p will be 90 degrees. Therefore, ∠q will also be 90 degrees, making q perpendicular to r.

So the statement that completes the proof is: q ⊥ r.

Answer 2

All the answers are in the attachment