Transcript 4.2 Shortcuts in Triangle Congruency

Warm up
No, corresponding sides
are not congruent, and
we can’t tell if the angles
are congruent.
No, the measures are
not the same
Yes, angle measures
are the same and the
rays go to infinity
Yes, all corresponding
sides are congruent and
all corresponding angles
are congruent.
Yes, all corresponding
parts are congruent.
JM
L   A
BA
WC
JF
KE
No, corresponding parts
are not congruent.
MX
NW
OP
PB
OC
4.2 Shortcuts in Triangle
Congruency
Remember last time…
We learned that two polygons were
congruent if EACH corresponding pair
of angles were congruent AND each
pair of corresponding sides were
congruent.
Remember that you had to
LIST EACH PAIR?
Yikes! That could get very long and
tedious (boring).
Today…
Today, you’re going to learn some shortcuts
that apply to TRIANGLES ONLY.
These shortcuts, if used correctly, will help
you prove triangle congruency.
Remember that congruency means EXACT
size and shape… don’t confuse it with
“similar”.
Side Side Side
If 2 triangles have 3 corresponding pairs of
sides that are congruent, then the triangles
X
~
AC = PX
are congruent.
AB ~
= PN
~
CB = XN
A
P
C
N
B
~
=
Therefore, using SSS,
~
∆ABC = ∆PNX
Side Angle Side
If two sides and the INCLUDED ANGLE in one
triangle are congruent to two sides and
INCLUDED ANGLE in another triangle, then the
triangles are congruent.
X
~
CA = XP
~
CB = XN
~
C = X
60°
A
P
C
60°
N
B
Therefore, by SAS,
~
∆ABC = ∆PNX
Angle Side Angle
If two angles and the INCLUDED SIDE of one
triangle are congruent to two angles and the
INCLUDED SIDE of another triangle, the two
triangles are congruent. X
~
CA = XP
~
A = P
~
C = X
60°
A
70°
70°
P
C
60°
N
B
Therefore, by ASA,
~
∆ABC= ∆PNX
Remembering our shortcuts
SSS
ASA
SAS
(just so you know, there are 2 abbreviations
that are not used for congruence: AAA
and SSA)
Let’s practice
I need 3 volunteers to hand out white
boards, markers and worksheets.
The worksheet is called ‘page 828’…
we’ll do section 4.2 together.
Your
Assignment
Pg 220-222: 1-3,
8-19,
23-29