5.1 – Perpendiculars and Bisectors. Perpendicular Bisector = a segment, ray, or line that… 1. Is perpendicular to another segment 2. Bisects that other.

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5.1 – Perpendiculars and Bisectors

Perpendicular Bisector = a segment, ray, or line that… 1. Is perpendicular to another segment 2. Bisects that other segment Equidistant = “equally distant” Vocab W HAT Line AW is a perpendicular bisector of segment HT A is equidistant from H and T

Perpendicular Bisector Theorem = Any point on the perp. bisector is equidistant from the endpoints of the segment. In the diagram below, WH = WT. Ex: Solve for x. Since WH = WT, our equation is x + 3 = 3x - 8. x = 5.5! W HAT x + 3 3x - 8

Vocab Angle Bisector = a segment, ray, or line that bisects an angle. NOTE: Distance between 2 objects is always measured perpendicular to the objects! S L A M Ray LM is an angle bisector of angle <SLA m<SLM = m<ALM

Angle Bisector Theorem = Any point on the angle bisector is equidistant from the sides of the angle. In the diagram below, MS = MA. M is equidistant from lines SL and LA. Ex: If SL = 12 and LM = 15, what is MS? Use Pythagorean Theorem! MS = 15 2 MS = 225 MS = 9! S L A M

Solve for x. 3x - 5 8x

Find m<LMA. 31 º S L A M º º º º 5. 49º

Assuming the figure is drawn to scale, which segment most likely represents the distance from A to the blue line? A 1. The red segment 2. The purple segment 3. The black segment 4. The orange segment