1.5 Notes Segment and Angle Bisectors
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Transcript of 1.5 Notes Segment and Angle Bisectors
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1.5 Notes• Segment and Angle Bisectors
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The point that divides (or bisects) a segment into two congruent segments.
A segment, ray, line, or plane that intersects a segment at its midpoint
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When given two points A (x1, y1) and B (x2, y2):
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Ex 1) Find the midpoint of DE with endpoints D(3,5) and E(-4, 0)
2
,2
2121 yyxxM
2
05,
2
43M
2
5,2
1M
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Ex 2) Find the midpoint of PQ with endpoints P(0, -7) and Q(-2, -1)
2
,2
2121 yyxxM
2
17,
2
20M
4,1 M
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Ex 3) The midpoint of XY is M(3, -4). One endpoint is Y(-3,-1). Find the coordinates of the other endpoint.
2
,2
2121 yyxxM
2
1,
2
3)4,3(
yx
2
33
x
36 xx9
2
14
y
18 yy 7
7,9
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Ex 4) The midpoint of JK is M(0, ½ ). One endpoint is J(2, -2). Find the coordinates of the other endpoint.
2
,2
2121 yyxxM
2
2,
2
2)2
1,0(
yx
2
20
x
20 xx 2
2
2
2
1 y
21 yy3
3,2
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A ray that divides (or bisects) an angle into two adjacent angles that are congruent
BD is an angle bisector so:
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Ex 5) JK bisects angle HJL. Given that HJL = 42o, what are the measures of the angles HJK and KJL?
42o
42/2 = 21o
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Ex 6) A cellular phone tower bisects the angle formed by the two wires that support it. Find the measure of the angle formed by the two wires.
47(2) = 94o
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Ex 7) In the diagram, MO bisects angle LMN. The measures of the two congruent angles are (3x – 20)o and (x + 10)o. Solve for x.
3x – 20 = x + 10
2x – 20 = 10
(3x – 20)o(x + 10)o
2x = 30
x = 15
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Ex 8) In the diagram BD bisect angle ABC. Find x and use it to find the measures of the angles ABD, DBC, and ABC.
2x + 50 = 5x + 5
50 = 3x + 5
45 = 3x
x = 15
ABD = 2(15) + 50
= 80o
=CBD
ABC = 80(2)
ABC = 160o