se the choices below to complete the proof.
Given: a⊥d , a⊥c
Prove: d∥c
Proof:
1. Given: a⊥d , a⊥c
2. Since a is perpendicular to d, then a and d form a right angle.
3. Since a is perpendicular to c, then a and c form a right angle.
4. If two lines form a right angle with the same line, then they are parallel to each other.
5. Therefore, d∥c.
To prove that d∥c, we need to show that the lines d and c are parallel.
Given: a⊥d, a⊥c
Proof:
1. Lines that are perpendicular to the same line are parallel.
(This is a property of perpendicular lines)
2. Line a is perpendicular to lines d and c.
(Given)
3. Therefore, lines d and c are parallel to each other.
(By using property 1 and line a as the common perpendicular line)
Hence, we have proved that d∥c.
To prove that d is parallel to c, we need to show that the lines formed by d and c do not intersect.
Given that a is perpendicular to both d and c, we can use the theorem that states if a line is perpendicular to two coplanar lines, then those two lines are parallel.
So, to complete the proof, we can use the following steps:
1. Start with the given information: a is perpendicular to d and a is perpendicular to c.
2. Apply the theorem that says if a line is perpendicular to two coplanar lines, then those two lines are parallel.
3. By applying the theorem, we conclude that d and c are parallel.
4. Therefore, we have proven that d is parallel to c.
By using the given information and applying relevant theorems, we were able to establish the parallel relationship between d and c.