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Perpendicular Lines

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

The symbol ⊥ means is perpendicular to .

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.

The rays P T → , T U → and T W → are perpendicular to each other.

Example :

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 ° .