use the choices below to complete the proof. given: a⊥d, a⊥c. prove d∥c

Answer 1

To prove that d∥c, we can use the fact that when two lines are perpendicular to the same line, they are parallel to each other.

Given that a⊥d and a⊥c, we can conclude that d∥c using the following steps:

1. Draw a line a and intersect it with lines d and c.
2. Given that a⊥d, we know that the angle formed between a and d is 90 degrees.
3. Similarly, given that a⊥c, we know that the angle formed between a and c is also 90 degrees.
4. Since d and c both form right angles with a, by the perpendicular transversal property, we can state that d∥c.
5. Therefore, we have proven that d∥c.

By using the fact that when two lines are perpendicular to the same line, they are parallel to each other, and given that a⊥d and a⊥c, we have successfully proven that d∥c.