6.1 Perpendicular and Angle Bisectors

What we will learn Use perpendicular bisectors to find measures Use angle bisectors to find measures Write equations for perpendicular bisectors

Needed vocab Equidistant: point that is same distance from all other points and sides

Ex. 1 Using perpendicular bisector thms Find each measure: 𝑅𝑆 SQ is perpendicular bisector by the marking, then PS = RS 6.8 𝐸𝐺 FH is perpendicular bisector by Thm 6.2 So EF = FG 19

Your practice Find x, DC, and AD 5𝑥=3𝑥+14 −3𝑥 −3𝑥 2𝑥=14 2𝑥 2 = 14 2 −3𝑥 −3𝑥 2𝑥=14 2𝑥 2 = 14 2 𝑥=7 DC = 35 AD = 35

Ex. 3 Angle bisectors Find angle GFJ Since J is equidistant from the rays and in interior of angle, then angle bisector 42 Find x, SP, and RS SQ is angle bisector by the markings, then point S is equidistant from rays 6𝑥−5=5𝑥 −6𝑥 −6𝑥 −5=−1𝑥 −5 −1 = −1𝑥 −1 5 = x, SP and RS = 25

Ex. 5 writing equation of perpendicular bisectors Write equation of perpendicular bisector of a segment with endpoints (-2,3) and (4,1). Midpoint: −2+4 2 , 3+1 2 = (1,2) Slope of segment: 𝑚= 1−3 4−(−2) = −2 6 = −1 3 Slope of perp. seg. is 3. Finding b: 2=3 1 +𝑏 2=3+𝑏 −3−3 −1=𝑏 Steps 1. find midpoint Mid = 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 2. find slope of segment Remember negative reciprocal of segment for perpendicular segment 3. find y-intercept (b) of new line Plug in m, x, and y into 𝑦=𝑚𝑥+𝑏 m is slope and x and y come from midpoint 4. plug in m and b into 𝑦=𝑚𝑥+𝑏 Perpendicular bisector equation: 𝑦=3𝑥−1