Question

PLZ help geometry proof. Will give Brainlyiest I’ve posted question 3 times so you can get triple the points

Answer 1

Answer:

The two column proof can be presented as follows;

Statement                     ${}$                   Reason

1. p║q                    ${}$                        Given

∠1 ≅ ∠11

2. ∠1 ≅ ∠9                     ${}$               Corresponding angles on parallel lines

3. ∠9 ≅ ∠11                    ${}$               Transitive property of equality

4. a║b                    ${}$                       Corresponding angles on parallel lines are congruent

Step-by-step explanation:

The statements in the two column proof can be explained as follows;

Statement                     ${}$                Explanation

1. p║q                    ${}$                        Given

∠1 ≅ ∠11

2. ∠1 ≅ ∠9                     ${}$               Corresponding angles on parallel lines crossed by a common transversal are congruent

3. ∠9 ≅ ∠11                    ${}$               Transitive property of equality

Given that ∠1 ≅ ∠11 and we have that ∠1 ≅ ∠9, then we can transit the terms between the two expressions to get, ∠9 ≅ ∠11 which is the same as ∠11 ≅ ∠9

4. a║b                    ${}$                       Corresponding angles on parallel lines are congruent

Whereby we now have ∠9 which is formed by line a and the transversal line q, is congruent to ∠11 which is formed by line b and the common transversal line q, and both ∠9 and ∠11 occupy corresponding locations on lines a and b respectively which are crossed by the transversal, line q, then lines a and b are parallel to each other or a║b.