use the choices below to complete the proof. given: a⊥d, a⊥c. prove d∥c
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.
To prove that d∥c, we need to show that the lines d and c are parallel. Given the information, a⊥d and a⊥c, we can use the properties of perpendicular lines and parallel lines to complete the proof.
Here are the choices that can be used to complete the proof:
1. If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.
2. If two lines are perpendicular to the same line, then they are parallel.
To determine which choice to use, let's analyze the given information.
The statement "a⊥d" means that line a is perpendicular to line d. Similarly, "a⊥c" means that line a is perpendicular to line c.
Since line a is perpendicular to both lines d and c, we can apply the first choice: If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.
Using this choice, we can conclude that since line a is perpendicular to line d, and line d is parallel to line c, then line a is also perpendicular to line c. Therefore, we can state that d∥c.
So, to complete the proof, we can use the choice: If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well. By applying this choice, we have successfully proven that d∥c based on the given information of a⊥d and a⊥c.
To prove that d∥c, we can use the fact that if two lines are perpendicular to the same line, then they are parallel to each other (the converse of the Perpendicular Transversal Theorem).
Given:
a⊥d
a⊥c
Proof:
1. Given: a⊥d (Given)
2. Given: a⊥c (Given)
3. If two lines are perpendicular to the same line, then they are parallel to each other (Perpendicular Transversal Theorem)
4. Therefore, d∥c (Conclusion from steps 1, 2, and 3)
Thus, we have proven that d∥c.