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 ⊥ mSince 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
