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5.1 Perpendicular and Angle Bisectors Name ____________________________________
Review:
Perpendicular Bisector : A line _________________________ to a segment at its ____________________________.
You try: Draw ๐๐พฬ
ฬ
ฬ
ฬ
. Draw line M that
that is the perpendicular bisector of ๐๐พฬ
ฬ
ฬ
ฬ
.
Angle Bisector : A ________ that divides an angle into two congruent ___________________.
You try: Draw โ ๐ด๐ต๐ถ. Draw ๐ต๐โโโโโ that is the
angle bisector.
Equidistant : When a point is the same ____________________ from two or more objects.
Angle Review:
1) Name three angles in the picture: ____________________ ______________________ ___________________
2) If ๐๐โโโโโโโ bisects โ ๐๐๐, then which two angles are congruent? ___________________________________
3) Draw obtuse โ ๐ถ๐ด๐. Draw the angle bisector ๐ด๐โโโโโ. 4) Name the numbered angles:
Which two angles are congruent? _________________________
***The middle letter of an angle represents the __________________!
D C
A
B
Perpendicular Bisector Theorem:
Examples:
1) YW = _____________ 2) BC = _______________ 3) PR = _______________
4) Given that line l is the perpendicular bisector 5) Given that DE = 20.8, DG = 36.4, and E
of ฬ
๐ท๐ธฬ
ฬ
ฬ
and EG = 14.6, then DG = ________________. EG = 36.4, then EF = _________________.
Summary:
Theorem Example Conclusion Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
Converse of the Angle Bisector Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.
Practice:
Find each measure.
1. RT ๏ฝ ________________ 2. AB ๏ฝ ________________ 3. HJ ๏ฝ ________________
- EH = ________________ 5. m๏ QRS = ______________ 6. m๏ WXZ = _____________
5.1 Practice B Name __________________
Perpendicular Bisectors and Angle Bisectors Date __________________________
Use the figure for #1-2.
- Given that line m is the perpendicular bisector of
FH and EH ๏ฝ 100, find EF. _________________
2.Given that EF ๏ฝ 13, FH ๏ฝ 10, and EH ๏ฝ 13, find GH. ________________
Use the figure for #3-6.
- Given that line p is the perpendicular bisector of XZ and XY ๏ฝ 15.5, find _ZY. ______________________
- Given that XZ ๏ฝ 38, YX ๏ฝ 27, and YZ ๏ฝ 27, find _ZW. ______________________
- Given that line p is the perpendicular bisector of XZ ; XY ๏ฝ 4 n , and YZ ๏ฝ 14, find n. _______________________
- Given that XY ๏ฝ ZY , WX ๏ฝ 6 x โ 1, and XZ ๏ฝ 10 x ๏ซ 16, find ZW. _______________________
Use the figure for Exercises #7-8. 7 .Given that ๐ฝ๐ฟฬ
bisects ๏ KJM and KL ๏ฝ 42, find ML. _________________
- Given that KL ๏ฝ 4 and ML ๏ฝ 4 and m๏ MJL ๏ฝ 40 o, find m๏ KJL. _________________
Use the figure for Exercises # 9 - 12.
- Given that FG ๏ฝ HG and m๏ FEH ๏ฝ 56 o, find m๏ _GEH. ______________________
- Given that ๐ธ๐บฬ
ฬ
ฬ
ฬ
bisects ๏ FEH and GF^ ๏ฝ 2,find _GH.
- Given that ๏ FEG ๏ ๏ GEH , FG ๏ฝ 10 z โ 30, and HG ๏ฝ 7 z ๏ซ 6, find _FG. ______________________
- Given that GF ๏ฝ GH , m๏ GEF ๏ฝ 8 a o, and m๏ GEH ๏ฝ 24 o, find a. ______________________
