warm-up—find the key steps
DESCRIPTION
Warm-Up—Find the Key Steps. Prove AB = CD A) B) C) D). X. O. D. C. A. B. Y. ANSWER TO 4-6 Side #1#2. Definition of Segment Bisector Vertical Angles are Congruent SAS CPCTC Vertical Angles are Congruent ASA CPCTC. SSS CPCTC Vert. Angles are Congruent ASA CPCTC - PowerPoint PPT PresentationTRANSCRIPT
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Warm-Up—Find the Key Steps Prove AB = CD
A)
B)
C)
D)
BOX DOY# #
BX DY
AB CD
A BO CD
X
Y
ABX CDY# #
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ANSWER TO 4-6 Side #1 #2
1) Definition of Segment Bisector
2) Vertical Angles are Congruent
3) SAS4) CPCTC5) Vertical Angles
are Congruent6) ASA7) CPCTC
1. SSS2. CPCTC3. Vert. Angles are
Congruent4. ASA5. CPCTC6. Supps to
congruent angles are congruent
#3 ASA
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Answers to 4-3 Side
#1 1)Given 2)Vert. Angles cong. 3) SAS 4) CPCTC
#2 1) Given 2) Corr. Angles are cong. 3) ASA4) CPCTC 5) corr. angles cong, then parallel
#3 1) Given 2) Def of mdpt. 3) Reflexive4) SSS 5) CPCTC 6) Def of <bisector
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4-7 MEDIANS, ALTITUDES, AND PERPENDICULAR BISECTORS
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MEDIAN
A segment from a vertex to the midpoint of the opposite side.
Median—Midpoint--Middle
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ALTITUDE
A perpendicular segment from a vertex to the opposite side.
Makes a 90 and comes from the vertex.
Acute Right Obtuse
This leg is the altitude
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PERPENDICULAR BISECTOR
A segment/ ray/ line that is perpendicular to the segment at its midpoint.
Combo: 90 AND Midpt Only one with 2 words and has 2things to look for
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THEOREM 3-5 If a point lies on the perpendicular bisector of a
segment, then it is equidistant from the endpoints of the segment.
P●
S● ●A
SP ____ PA
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THEOREM 3-6 (CONVERSE OF 3-5)
If a point is equidistant from the endpoints of the segment, then it is on the __________________________ of the segment.
perpendicular bisector
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THEOREM 3-7 If a point lies on the bisector of an angle,
then it is equidistant from the __________ of the angle. If BP bisects <B, then
______=______ .
If MP = PN, then P lies on
the ____________________
of <B.
Converse: If a point is equidistant from the sides of an angle, then it lies on the ________
_____________ of the angle.
P
A●
B● C
M●
●
N
MP PN
BB
A●
B
A●
B
A●
B● C
A●
B
sides
● C
A●
B
angle bisector
angle bisector
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Practice
1. Given: P is on the perpendicular bisector of XY. P is equidistant from _____ and _____.
2. If P is equidistant from ______ and ______, then ______=_______ .
X● ●Y
X Y
P●
X Y
XM MY
M
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Practice
3. If P is on the angle bisector of <DEF, then P is equidistant from ______ and _____.
DE
E
D●
●F
P●
EF
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Practice
4. If LN bisects <JLK, then N is equidistant from ______ and ______ .
5. If O is the midpoint of LK and JO LK , then: a) P is equidistant from ____ and _____.
b) and JO is the _____________________ of LK.
J N
K
O
L
M
P●
LJ LK
L K
perpendicular bisector
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Practice6. If ,then KM is
a(n) _____________ of JKL.
7. If LO = OK, then JO is a (an) ____________ of JKL.
8. If P is equidistant from K and L, then P is on the _____________________ of LK.
9. If O is equidistant from JL and JK , then O is on the _____________________ of <J.
KM LJ
L
O
KJN
MP●
altitude
median
perpendicular bisector
angle bisector
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Homework
Worksheet 4-7