Perpendicular Bisector Theorem:
CD is the bisector of Δ ABC CD is the bisector or AB CD is the bisector of ACB Perpendicular Bisector Theorem If a point is on the bisector of a segment, then it is equidistant from the endpoints of the segments. C A D B Δ ADC Δ BDC by SAS Any point on CD is the same distance from Pt. A and from Pt. B
Converse of the Perpendicular Bisector Theorem:
Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the bisector of the segments. Locus Theorems – A set of points that satisfy a given condition.
Slide 4:
** Distance from a point to a line is the length of the perpendicular segment from the point to the line. P A D B The distance from P to AB is the length of PD.
Th(5 – 4) Bisector Thm.:
Th(5 – 4) Bisector Thm. If a point is on the bisector of an , then the point is equidistant from the sides of the . A B C D ABD CBD The distance from D to AB is AD The distance from D to BC is DC Δ ABD Δ CBD by AAS AB CB and AD CD 1 2 1 2
Slide 6:
A B C
Example 2::
Example 2: B C D F 2x + 24 5x Find FD 5x = 2x + 24 3x = 24 x = 8 FD = 2x + 24 = 2(8) +24 = 16 + 24 = 40
Slide 8:
B C D F Example 3: 2x (x + 20) Find m BCD 2x = x + 20 x = 20 m BCF = 2x = 2(20) = 40 m BCD = 2m BCF = 2(40) = 80 40 40 80
Slide 9:
Page 267 1-48 Skip any 4