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.
