FINAL EXAM REVIEW
Chapter 4
Key Concepts
Chapter 4 Vocabulary
congruent figures
corresponding parts
equiangular
Isosceles Δ
legs
base
vertex angle
base angles
median
altitude
perpendicular bisector
regular polygon
CONGRUENCE METHODS:
SSS
SAS
ASA
AAS
HL
Defn. of Congruent Triangles

• Two triangles are congruent (
) if and only
if their vertices can be matched up so that the
corresponding parts (angles and sides) of the
triangles are congruent.
∆ ABC  ∆ DEF
7
C
AB
BC
B
C
E
F
CA
D
E
7
7
B






7
D
7
A
A
7
ORDER MATTERS!
F
DE
EF
FD
SSS Postulate
If three sides of one triangle are congruent to three sides of
another triangle, then the triangles are congruent.
S
B
A
R
C
~
ABC =
T
RST by SSS Post.
SAS Postulate
If two sides and the included angle of one triangle are congruent
to two sides and the included angle of another triangle, then the
triangles are congruent.
F
Q
E
P
G
EFG ~
=
R
PQR by SAS Post.
ASA Postulate
If two angles and the included side of one triangle are congruent
to two angles and the included side of another triangle, then the
M
triangles are congruent.
Y
N
Z
L
X
XYZ ~
=
LMN by ASA Post.
The AAS (Angle-Angle-Side)
Theorem
If two angles and a non-included side of one triangle
are congruent to the corresponding parts of another
triangle, then the triangles are congruent.
ABC

B
XYZ
C
A
X
Y
Z
The HL (Hypotenuse - Leg)
Theorem
If the hypotenuse and a leg of one right triangle are
congruent to the corresponding parts of another right
triangle, then the triangles are congruent.
ABC

A
X
XYZ
B
C
Y
Z
Summary of Ways to Prove Triangles
Congruent
All triangles
SSS Post
SAS Post
ASA Post
AAS Thm
Right triangles
HL Thm
The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then
the angles opposite those sides are
congruent.
Iso.
Thm.
Converse to Isosceles Triangle Theorem
If two angles of a triangle are congruent, then
the sides opposite those angles are
congruent.
Converse to Iso.
Thm.
Corollaries
• An equilateral triangle is also equiangular.
• An equilateral triangle has three 60o
angles.
The bisector of the vertex angle of an
isosceles triangle is perpendicular to the
base at its midpoint.
•
Median

A median of a triangle is a segment from
a vertex to the midpoint of the opposite
side. Each triangle has three medians.
A
A
.
A
C
.
B
C
.
C
B
B
Altitude

The perpendicular segment from a vertex to
the line that contains the opposite side.
A
C
A
Acute Triangles
Right Triangles
A
B
B
C
A
C
B
Obtuse Triangles
A
B
A
C
B
C
A
C
B
C
A
B
B
C
C
A
B
Perpendicular Bisector

A line, ray, or segment that is
perpendicular to a segment at its
midpoint.
Theorem
• If a point lies on the perpendicular bisector of a segment, then…
the point is equidistant from the endpoints of the segment.
.
.
.
CONVERSE:
If a point is equidistant from the endpoints of a segment, then… the point lies
on the perpendicular bisector of the segment.
Theorem
• If a point lies on the bisector of an angle then,…
the point is equidistant from the sides of the angle.
.
CONVERSE:
If a point is equidistant from the sides of an angle, then…..the point lies on the
bisector of the angle.
• CPCTC
Homework
► Chapter
3-4 Review Olympics W/S
► pg. 164 #1-9 (multiple choice)