Using the diagram above, we can rewrite the theorem as follows.
Given:& l ⊥ m
Prove:& ∠1 ≅ ∠2, ∠2 ≅ ∠4,
& ∠3 ≅ ∠4, and ∠1 ≅ ∠3
Now we are ready to start the proof by using two-column proof table.
We will prove this theorem without using two-column proof table. Let's consider the figure above. We know that the lines are perpendicular. Since we have a theorem that perpendicular lines intersect to form four right angles, the angles ∠1, ∠2, ∠3, and ∠4 are right angles. Also by the definition of the right angles, we can write the following equations. m∠1 = 90 ^(∘)
m∠2 = 90 ^(∘)
m∠3 = 90 ^(∘)
m∠4 = 90 ^(∘)
We will use the Substitution Method to prove the congruent angles.
We can also use the Substitution Method to show the other congruent angles. m∠1 = m∠2
m∠2 =m∠4
m∠3 =m∠4
m∠1 =m∠3
To show the congruence, we will use the definition of the Congruent Angles. m∠1 ≅ m∠2
m∠2 ≅ m∠4
m∠3 ≅ m∠4
m∠1 ≅ m∠3
We reach the conclusion of what we wanted to prove.
