Download Chapter 4 gal lour

Chapter 4 gal lour!
Proofs with * may be key stepped. All others should be done in
a full 2 column fashion. Know all of your previous theorems,
postulates and definitions as well as the new ones from chapter 4:
Theorems:
SSS, SAS, AAS, ASA, HL
Isosceles Triangle Theorem (If 2 sides congruent, opp angles congruent)
Iso Triangle con: If 2 angles congruent, opp sides congruent
Equilateral triangle has three 60 degree angles
Angle bisector of vertex angle on isosceles triangle is also a perpendicular bisector to the
opposite side
A point lies on the perpendicular bisector of a segment, if and only if the point is
equidistant from the endpoints of the segment.
A point lies on the bisector of an angle if and only if it is equidistant from the sides of the
angle.
Vocabulary:
Median, Altitude, Perpendicular bisector, Isosceles
1. Identify each line (not part of ABC ) as
an altitude, a median and a perpendicular
bisector.
A
Draw all three altitudes.
B
C
E
2
1
2.
A
S
5
3
T
4
B
Solve if you have enough information.
If 1  3 , then which segments must be congruent? ______________________
If ES  ET , m2  75, m5  3x , then x = ________
If 2, 5 supplements. ES = 3y+5, and ET = 25 – y, then y = __________
L
B
F
M
J
K
D
3. If M is on the perpendicular bisector of JL , then M is equidistant from ___________
and ____________
If M is on the perpendicular bisector JK , then ________ = ____________
If M is equidistant from K and L, then M is on the _________________
E
D
G
4. Given: AD, BE bisect each other at C
Prove: GC  FC
C
A
F
B
P
*5. Given:
HNI is isosceles with base
HI ; LI and HK are medians
of HPI ;
NJ is altitude of HNI
Prove: LM  MK
M
K
L
N
H
J
I
N
*6. Given: PN // MQ , MS  PR
P
R
PN  MQ
Prove: NMS  QPR
S
M
Q
L
P
O
Q
K
N
a. LN is a median. KNL  MNL
___________
b. LN is an altitude. KNL  MNL
___________
c. LN is a perpendicular bisector.
KNL  MNL ___________
M
7. Identify the theorem or postulate that
can be used, if any, to prove the following
triangles congruent. If you cannot prove
the triangles congruent, put an “X” on the
line.
d. LN is angle bisector of KLM ;
KLM is an isosceles with base KM .
KNL  MNL ___________
e. KO and PM are medians of
isosceles KLM .
PQK  OQM __________
A
1
Given: AB // DC ; AD // BC
B
2
Prove: AE  CE; DE  BE
E
4
D
*8.
3
C
Given: 1  2; AE  BD
Prove: 5  6
A
1 2
3 4
B
C
D
5 6
E
9.
10.
U
N
In the figure to the left, PU = PT,
U , T are right angles, and
mPNU  5(mNPT ) and
PUN  PTN
Find mNPT .
P
T
T
S
11.
12.
M
Given: MTO is equilateral; TN bisects
MTO . Which of the following cannot
be proved with the given information?
a. S and P are midpoints.
b. TN  MO
c. M  O  MTO
d. N is the midpoint of MO
P
N
O
With congruences shown, Solve for x.
x
145
Given the figure to the left, which one of
the following can be used to prove the
triangles congruent?
x
x
13.
L
M
Q
P
R
14.
O
N
a. AAS only
b. HL only
c. AAS or SAS
d. Not congruent
In the picture, LPM  NPO ; Name
three other pairs of triangles that can be
proved congruent.