Bell WorkWednesday, August 7, 2013
List two acts that will results in a student having a teacher conference.
Standard
• Congruency postulates, SSS, SAS, ASA, & AAS
Essential Question
• How does learning the congruency postulates help me prove that two triangle are congruent?
Closing
• See nature by numbers video:http://www.youtube.com/watch?v=kkGeOWYOFoA
• Homework Assignment #1 – You saw the video, Nature by Numbers. Submit a picture of something from nature and point out one or several geometric shapes similarly to what you saw in the video. Due: Thursday in class.
The congruence
postulates:SSS, SAS, ASA, & AAS
Proving Triangles Congruent
Two geometric figures with exactly the same size and shape.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
F
How much do you How much do you need to know. . .need to know. . .
. . . about two triangles to prove that they are congruent?
You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
Corresponding PartsCorresponding Parts
ABC DEF
B
A C
E
D
F
1. AB DE
2. BC EF
3. AC DF
4. A D
5. B E
6. C F
Do you need Do you need all six ?all six ?
NO !
SSSSASASAAAS
Side-Side-Side (SSS)Side-Side-Side (SSS)
1. AB DE
2. BC EF
3. AC DF
ABC DEF
B
A
C
E
D
F
Side-Angle-Side (SAS)Side-Angle-Side (SAS)
1. AB DE
2. A D
3. AC DF
ABC DEF
B
A
C
E
D
F
included angle
The angle between two sides
Included AngleIncluded Angle
G I H
Name the included angle:
YE and ES
ES and YS
YS and YE
Included AngleIncluded Angle
SY
E
E
S
Y
Angle-Side-Angle-Side-AngleAngle (ASA) (ASA)
1. A D
2. AB DE
3. B E
ABC DEF
B
A
C
E
D
F
included
side
The side between two angles
Included SideIncluded Side
GI HI GH
Name the included side:
Y and E
E and S
S and Y
Included SideIncluded Side
SY
E
YE
ES
SY
Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)
1. A D
2. B E
3. BC EF
ABC DEF
B
A
C
E
D
F
Non-included
side
Warning:Warning: No SSA Postulate No SSA Postulate
A C
B
D
E
F
NOT CONGRUENT
There is no such thing as an SSA
postulate!
Warning:Warning: No AAA Postulate No AAA Postulate
A C
B
D
E
F
There is no such thing as an AAA
postulate!
NOT CONGRUENT
The Congruence PostulatesThe Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence
Name That PostulateName That Postulate
SASSASASAASA
SSSSSSSSASSA
(when possible)
Name That PostulateName That Postulate(when possible)
ASAASA
SASASS
AAAAAA
SSASSA
Name That PostulateName That Postulate(when possible)
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSSS
AA
HW: Name That PostulateHW: Name That Postulate(when possible)
(when possible)HW: Name That PostulateHW: Name That Postulate
Let’s PracticeLet’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
B D
For AAS: A F
AC FE
HWHWIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS:
Write a congruence statement for each pair of triangles represented.
A
B
FC
E
D
Slide 1 of 2
Slide 1 of 2
Before we start…let’s get a few things straight
INCLUDED SIDE
A B
C
X Z
Y
Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side
Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included
} Your Only Ways To Prove Triangles Are
Congruent
Overlapping sides are congruent in
each triangle by the REFLEXIVE property
Vertical Angles
are congruen
t
Alt Int Angles are congruent
given parallel
lines
Things you can mark on a triangle when they aren’t marked.
Ex 1
statement. congruence a Write.
and ,, and In
LE
NLDENDΔLMNΔDEF
DEF NLM
Ex 2
What other pair of angles needs to be marked so that the two triangles are congruent by AAS?
F
D
E
M
L
N
NE
Ex 3
What other pair of angles needs to be marked so that the two triangles are congruent by ASA?
F
D
E
M
L
N
LD
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
ΔGIH ΔJIK by AAS
G
I
H J
KEx 4
ΔABC ΔEDC by ASA
B A
C
ED
Ex 5
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
ΔACB ΔECD by SAS
B
A
C
E
D
Ex 6
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
ΔJMK ΔLKM by SAS or ASA
J K
LM
Ex 7
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
Not possible
K
J
L
T
U
Ex 8
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
V
Slide 2 of 2
Slide 2 of 2
Slide 2 of 2
Slide 2 of 2
Slide 1 of 2
(over Lesson 5-5)
Slide 1 of 2
(over Lesson 5-5)
Slide 1 of 2
Slide 1 of 2
Slide 1 of 2
Slide 1 of 2
Slide 2 of 2
Slide 2 of 2
Slide 2 of 2
Slide 2 of 2