Given: Line AB is perpendicular to line CD
Line AE is perpendicular to line CD
Prove: Line AB is parallel to line AE
Proof:
Statements Reasons
1. Line AB is perpendicular to line CD Given
2. Line AE is perpendicular to line CD Given
3. ∠ABD and ∠AED are right angles Definition of perpendicular lines
4. ∠ABD ≅ ∠AED Definition of congruent angles
5. AB || AE Definition of parallel lines
In step 1, we are given that line AB is perpendicular to line CD, and in step 2, we are given that line AE is perpendicular to line CD. In step 3, we use the definition of perpendicular lines to state that ∠ABD and ∠AED are right angles. In step 4, we use the definition of congruent angles to state that ∠ABD and ∠AED are congruent. Finally, in step 5, we use the definition of parallel lines to conclude that line AB is parallel to line AE. Therefore, the theorem is proven.
Write a paragraph proof of Theorem 3-8: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
The information and diagram for a two column proof is shown.
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1 answer