Obj. 14 Perpendicular Lines

The student will be able to (I can):

• Solve problems using perpendicular lines

• Set up and solve inequalities using the distance from a point to a line

Perpendicular Transversal Theorem

If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular.

∠1 ≅ ∠2 ⇒ m ⊥ n

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

n � p & n ⊥q⇒ p ⊥ q

1 2m

n

n

p

q

Distance From a Point to a Line

If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

r ⊥ t & s ⊥t⇒ r � s

The distance from a point to a line is the length of the perpendicular segment from the point to the line.

The distance from A to the line t is AB

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ssss

tttt

AAAA

BBBB

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Example Solve to find x and y in the diagram.

10x = 90

x = 9

8(9) + 4y = 90

4y = 18

y = 4.5

(8x+4y)°

(10x)°

Distance From a Point to a Line

1. Name the shortest segment from R to FO.

Since RG ⊥ FO, RG is the shortest segment

2. Write and solve an inequality for x.

FR > RG

x + 5 > 9

x > 4

F G O

R

x + 5x + 5x + 5x + 5 9999