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Which of the following completes the two-column proof below?

Given: ∠1≅∠2, p⊥r
Prove: q⊥r
Proof:

1. ∠1≅∠2 (Given)

2. p��q (?)

3. p⊥r (?)

4. q⊥r (?)

The figure shows lines p and q and transversal r. The intersection of line p and transversal r forms four angles, the top right angle is labeled as a right angle, the top left angle is labeled as 1. The intersection of line q and transversal r forms four angles, the bottom right angle is labeled as 2.

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akposevictor

2. Converse of corresponding angles theorem.

3. Given

4. Perpendicular transverse theorem

What is the Converse of Corresponding Angles Theorem?

According to the converse of corresponding angles theorem, if two corresponding angles are congruent, then the lines cut by the transversal that both angles line on are parallel to each other.

Thus, given that ∠1 ≅ ∠2, lines p and q will be parallel based on the converse of corresponding angles theorem.

We are given that lines p and r are perpendicular to each other, therefore, we can conclude that, based on the perpendicular transverse theorem, q⊥r.

The missing reasons in the proof are:

2. Converse of corresponding angles theorem.

3. Given

4. Perpendicular transverse theorem

Learn more about the converse of corresponding angles theorem on:

https://brainly.com/question/10565830

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