1. 6.1 Perpendicular and Angle Bisectors

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

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

4. 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

5. 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

6. 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

7. 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 , = (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