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# #

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

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

4-7 MEDIANS, ALTITUDES, AND PERPENDICULAR BISECTORS

MEDIAN

A segment from a vertex to the midpoint of the opposite side.

Median—Midpoint--Middle

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

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

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

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

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

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

Practice

3. If P is on the angle bisector of <DEF, then P is equidistant from ______ and _____.

DE

E

D●

●F

P●

EF

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

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

Homework

Worksheet 4-7