Perpendicular Lines

Perpendicular lines are lines, segments or rays that intersect to form right angles.

The symbol $⊥$ means is perpendicular to .

Math diagram

In the figure,

$P R ⊥ Q S$

The right angle symbol in the figure indicates that the lines are perpendicular.

In three dimensions, you can have three lines which are mutually perpendicular.

Math diagram

The rays $\vec{P T}, \vec{T U}$ and $\vec{T W}$ are perpendicular to each other.

Example :

Math diagram

If $A B ⊥ C D$ , find $m ∠ E O D$ .

Since $A B ⊥ C D$ , $m ∠ B O D = 90 °$ .

By the Angle Addition Postulate,

$m ∠ B O E + m ∠ E O D = m ∠ B O D$

Let $x °$ be the measure of $∠ E O D$ .

Then,

$35 ° + x ° = 90 °$ .

Subtract $35 °$ from each side.

$x ° = 55 °$

Therefore,

$m ∠ E O D = 55 °$ .