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12.) Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer. Pleaseee helppp

12.) Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer. Pleaseee helppp class=

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Answer:

Step-by-step explanation:

            Given                  Parallel lines                     Converse

a. ∠13 ≅ ∠17                          a║c                  Corresponding angles

b. ∠4 ≅ ∠9                            d║e                  Exterior alternate angles

c. m∠20 + m∠21 = 180°        a║b                  Consecutive interior angles

d. ∠8 ≅ ∠19                                                    Vertical angles

e. ∠10 ≅ ∠23                         b║c                  Interior alternate angles

f.  m∠14 + m∠17 = 180°          a║c                  Consecutive interior angles

aksnkj

From the given diagram and information, it can be concluded that lines a, b, and c are parallel, and lines d and e are parallel.

The given lines in the diagram are a, b, c, d, and e.

a. It is given that the measure of angle 13 is equal to that of angle 17.

Now, these two angles are made by lines a, c, and d. Now, the angles are corresponding and equal, and hence, lines a and c will be parallel.

b. It is given that the measure of angle 4 is equal to that of angle 9.

These two angles are made by lines d, e, and b. Now, the angles are alternate exterior and equal, and hence, lines d and e will be parallel.

c. It is given that the sum of the measure of angles 20 and 21 is equal to 180 degrees.

These two angles are made by lines a, b, and e. Now, the angles are supplementary and their sum is 180 degrees, and hence, lines a and b will be parallel.

d. It is given that the measure of angle 8 is equal to that of angle 19.

These two angles are vertically opposite angles between lines a and e.

e. It is given that the measure of angle 10 is equal to that of angle 23.

These two angles are made by lines b, c, and e. Now, the angles are alternate interior and equal, and hence, lines b and c will be parallel.

f. It is given that the sum of the measure of angles 14 and 17 is equal to 180 degrees.

These two angles are made by lines a, c, and d. Now, the angles are supplementary and their sum is 180 degrees, and hence, lines a and c will be parallel.

Therefore, it can be concluded that lines a, b, and c are parallel, and the lines d and e are parallel.

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