Perpendicular lines intersect to form four right angles
Practice makes perfect
Let's begin by writing the given information and what we want to prove.
Given:& ∠ 2 is a right angle
Prove:& l ⊥ m
Since perpendicular lines intersect to form four right angles, to prove that l⊥ m we will prove that ∠ 1, ∠ 2, ∠ 3 and ∠ 4 are all right angles. Before starting the proof, let's make a diagram that illustrates the given situation.
Remember that the measure of a right angle is equal to 90.
Statements
Reasons
1.
∠ 2 is a right angle
1.
Given
2.
m∠ 2=90
2.
Definition of right angle
3.
m∠ 1+m∠ 2=180
3.
Supplement Theorem
4.
m∠ 1+90=180
4.
Substitution Method
5.
m∠ 1=90
5.
Subtraction Property of Equality
6.
∠ 2 ≅ ∠ 3
6.
Vertical Angles Theorem
7.
m∠ 3=90
7.
Substitution Method
8.
∠ 1 ≅ ∠ 4
8.
Vertical Angles Theorem
9.
m∠ 4=90
9.
Substitution Method
10.
l ⊥ m
10.
Perpendicular lines intersect to form four right angles
