We need to prove one of the Right Angle Theorems, which states the following.
All right angles are congruent.
To do so, we will use the given figure.
Using the diagram, we can rewrite the theorem as follows.
Given:& ∠ 1, ∠ 2, ∠ 3 and ∠ 4 are right angles
Prove:& ∠ 1 ≅ ∠ 2 ≅ ∠ 3 ≅ ∠ 4
Remember, the measure of a right angle is 90. Now we are ready to start the two-column proof.
Statements
Reasons
1.
∠ 1, ∠ 2, ∠ 3 and ∠ 4 are right angles
1.
Given
2.
m∠ 1 = 90, m∠ 2 = 90, m∠ 3 = 90, and m∠ 4 = 90
2.
Definition of Right Angle
3.
m∠ 1 = m∠ 2 = m∠ 3 = m∠ 4
3.
Substitution Method
4.
∠ 1 ≅ ∠ 2 ≅ ∠ 3 ≅ ∠ 4
4.
Definition of Congruent Angles
Alternative Solution
Another Way
Here, we will prove this theorem without using two-column proof table. Let's consider the figure above. We know that 1, 2, 3, and 4 are right angles. By the definition of the right angle, we can write the measures of the angles.
m∠ 1 = 90 ^(∘)
m∠ 2 = 90 ^(∘)
m∠ 3 = 90 ^(∘)
m∠ 4 = 90 ^(∘)
We will use the Substitution Method to prove the congruence.
We can also use the Substitution Method to show the other congruent angles. m∠ 1 = m∠ 2 = m∠ 3 =m∠ 4
To show the congruence, we will use the definition of the Congruent Angles. m∠ 1 ≅ m∠ 2 ≅ m∠ 3 ≅ m∠ 4
We reach the conclusion of what we wanted to prove.
