Download Chapter 4 gal lour

Chapter 4 gal lour!
All work and proofs must be done on a separate piece of paper
to receive credit. Proofs with * may be key stepped. All others
should be done in a full 2 column fashion. As always, the
standard is 100%. 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 a. Identify each line (not part of
ABC ) as an altitude, a median and a
perpendicular bisector
b. Draw all three altitudes.
A
B
C
E
2
1
2.
A
5
3
4
T
S
B
Solve
If 1  3 , then which segments must be congruent? ____________________
a.
b. Let ES  ET , m2  75, m5  3x , then x = ________
c. Given: 2 and 5 supplements, 1  4 .
AE = 2x + 3y - 1, ES = 2x + 2y, ET = 5x – y +3 and EB = -3x + 5y + 6.
x = _______________, y = _________________
L
B
F
M
J
K
D
3.
a. If M is on the perpendicular bisector of JL , then M is equidistant from
___________ and ____________
b. If M is on the perpendicular bisector JK , then ________ = ____________
c. 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
L
M
Q
P
R
O
N
5. In the picture, LPM  NPO ; Name
three other pairs of triangles that can be
proved congruent.
N
*6. Given: PN // MQ , MS  PR
P
R
PN  MQ
Prove: NMS  QPR
S
M
Q
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.
L
P
O
Q
K
N
M
KNL  MNL
a. LN is a median.
___________
d. LN is angle bisector of KLM ;
KLM is an isosceles with base KM .
KNL  MNL ___________
KNL  MNL
b. LN is an altitude.
___________
e. KO and PM are medians of
isosceles KLM .
PQK  OQM __________
c. LN is a perpendicular bisector.
KNL  MNL ___________
A
1
8. Given: AB // DC ; AD // BC
B
2
Prove: AE  CE; DE  BE
E
4
D
3
C
U
N
P
T
9. 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 .
10. Given: MTO is equilateral; TN
bisects MTO . Which of the following
cannot be proved with the given
information?
T
S
a. S and P are midpoints.
b. TN  MO
c. M  O  MTO
d. N is the midpoint of MO
P
M
N
O
11. With congruences shown, Solve for x.
x
145
12. Given the figure to the left, which one
of the following can be used to prove the
triangles congruent?
x
x
a. AAS only
b. HL only
c. AAS or SAS
d. Not congruent