Geometry 14 Nov 2012
WARM UP1) sketch and label
vertex angle
base angles
remote interior angles
exterior angle
adjacent interior angle
Find measures of all angles
if x = 140⁰. Show work.
B
X
2)
A
C
objective
Students will explore and apply triangle
inequalities and congruency shortcuts.
Students will take notes, do a whole class
investigation and work problems collaboratively.
Homework- all accepted Nov 16 for full credit
Please √ if correct X if incorrect for ALL!!
Homework due TUES, Nov. 6: 4.2: 6 – 10, 18 – 21
4.3: Investigation 2
Homework due FRIDAY, Nov. 9 (please CHECK)
4.3, page 218+: 5 – 10,
19 and 20 (use handout), 21 - 23
Homework due Tuesday, Nov 13:
• create a rap, song, poem, short story, other?
as an aid to help you remember 5 – 8 of our chapter 4
vocabulary definitions AND TWO chapter 4 conjectures
• Bring a picture of a house or structure
• Complete Nov 6 Angle Chase Warm up/ CSAP
(both sides) if not completed in class
• Complete Nov. 9 CW, Lines, Angles and Triangles
(both sides) if not completed in class.
HOMEWORK DUE FRIDAY, Nov. 16:
• 4.4, page 224: 1- 3, 19 (sketch on graph paper)
• 4.5, page 229: 1 – 3, 18
• Complete Worksheet- Congruent Triangles
Chapter 4 TEST– TUESDAY, Nov. 20
THERE WILL BE NO HOMEWORK ASSIGNED OVER
THE THANKSGIVING BREAK!!
Projects and Quizzes
Quiz- Corrections- Optional HW assignment by Nov 20
Write problem done incorrectly
Explain what is incorrect
Do/explain how to do the problem correctly
Shuttling Around- REVISIONS accepted through
November 30th!
MAKE SURE ANY CHANGES ARE EXTREMELY OBVIOUS 
I don’t have time to re-read your whole project!! 
(use different color, notes, etc.)
Your task
You have 15 minutes to work with your
classmates to find and correct your errors!
1) Write the problem on a piece of notebook paper.
2) Identify what you did incorrectly.
3) EXPLAIN how to do the problem correctly.
RE-DO the problem correctly on your paper!
EVERYONE must correct a minimum of 5 problems --to be submitted in 15 minutes!
If you did not miss five, work with a classmate to help
them find THEIR errors, write their problem on your
paper, explain their error and show corrected work!
Term
Triangle
Inequality
Conjecture
Side-Angle
Inequality
Conjecture
Triangle
Exterior
Angle
Conjecture
Conjecture
The sum of the lengths
of any two sides of a
triangle is greater than
the length of the 3rd
side
In a triangle, if one side is
longer than another side,
then the angle opposite the
longer side is the largest
angle.
The measure of an exterior
angle of a triangle is equal to
the sum of the measures of
the two remote interior
angles
Examples
#1
Determine whether it is possible for a
triangle to have sides measuring…….
explain briefly
9cm,13cm, 23cm
15cm,10cm, 24cm
# 2 Arrange the lettered measures in order from
c
greatest to least:
24cm
0
c
35
740
a
b
18cm
b
22cm
a
a
Triangle Congruency Shortcuts
Whole Class Discussion- popsicle sticks
Triangle Congruency Shortcuts
SSS, ASA, SAS, AAS
SSA and AAA do not guarantee CONGRUENCY:
“not enough information”
SSA (bad word spelled backwards ≠ shortcut!)
http://www.algebra.com/algebra/homework/Geometry-proofs/Geometry_proofs.faq.question.389765.html
AAA– SIMILAR but not necessarily congruent!
http://hs.doversherborn.org/hs/koman/Geometry/Notes/DiscoveringGeometry/Chapter%205%20%20Triangle%20Properties/5-5/5-5notes.htm
Proving Triangles
Congruent
The Idea of a Congruence
Two geometric figures with
exactly the same size and
shape.
F
B
A
C
E
D
How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?
Corresponding Parts
In previous lessons, you learned that if all
six pairs of corresponding parts (sides
and angles) are congruent, then the
triangles are congruent.
1. AB  DE
2. BC  EF
3. AC  DF
4.  A   D
5.  B   E
6.  C   F
ABC   DEF
Do you need all six ?
NO !
SSS
SAS
ASA
AAS
Triangle congruence shortcuts
see page 221
“included” and “adjacent”
SSS Congruence
shortcut
SAS Congruence
shortcut
Side – Side- Side
Side – included Angle - Side
Side-Side-Side (SSS)
1. AB  DE
2. BC  EF
3. AC  DF
ABC   DEF
Side-Angle-Side (SAS)
1. AB  DE
2. A   D
ABC   DEF
3. AC  DF
included
angle
Included Angle
The angle between two sides
G
I
H
Included Angle
Name the included angle:
E
Y
S
YE and ES
E
ES and YS
S
YS and YE
Y
Angle-Side-Angle (ASA)
1. A   D
2. AB  DE
ABC   DEF
3.  B   E
included
side
Included Side
The side between two angles
GI
HI
GH
Included Side
Name the included side:
E
Y
S
Y and E
YE
E and S
ES
S and Y
SY
Angle-Angle-Side (AAS)
1. A   D
2.  B   E
ABC   DEF
3. BC  EF
Nonincluded
side
Warning: No SSA Postulate
There is no such
thing as an SSA
postulate!
E
B
F
A
C
D
NOT necessarily CONGRUENT
Warning: No AAA Postulate
There is no such
thing as an AAA
postulate!
E
B
A
C
D
F
NOT necessarily CONGRUENT
The Congruence Shortcut
Conjectures
 SSS
correspondence
 ASA
correspondence
 SAS
correspondence
 AAS
correspondence
 SSA correspondence
 AAA
correspondence
Chapter 4 Triangles
Term
Definition
Example
SSS
Congruence
Shortcut
If three sides of one triangle
are congruent to three sides of
another triangle, then the
triangles are congruent
SAS
Congruence
Shortcut
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
Isosceles ΔABC
DOES NOT guarantee
B  C
congruency
SSA
A
AD  AD
B
D
C
BAD  CAD
90o
Chapter 4 Triangles-Term
Definition
ASA
Congruence
Shortcut
SAA
Congruence
Shortcut
AAA
If two angles and the included
side of one triangle are
congruent to two angles and
the included side of another
triangle, then the triangles are
congruent.
If two angles and a nonincluded side of one triangle
are congruent to the
corresponding two angles and
non-included side of another
triangle, then the triangles are
congruent
DOES NOT guarantee
congruency
Example
Chapter 4 Triangles-Term
Definition
ASA
Congruence
Shortcut
SAA
Congruence
Shortcut
AAA
If two angles and the included
side of one triangle are
congruent to two angles and
the included side of another
triangle, then the triangles are
congruent.
If two angles and a nonincluded side of one triangle
are congruent to the
corresponding two angles and
non-included side of another
triangle, then the triangles are
congruent
DOES NOT guarantee
congruency
Example
Chapter 4 Triangles-Term
Definition
Example
Hypotenuse If an hypotenuse
- Leg
and a leg of two
Congruenc
right triangles
e Shortcut
are congruent,
the triangles are Proof: if ΔABC and ΔDEF
are both right triangles
congruent.
2
2
2
Then AC + CB = AB
and DF2 + FE2 = ED2
if AC = DF and AB = DE
Then BC = EF
and the triangles are
congruent by
SSS congruence
If two triangles
are back to back –
they share a
common SIDE
“same side”
A
B
AB CD
C
If two triangles meet at
a vertex– vertical
angles are congruent
D
If two triangles meet at a
vertex– and the sides are
parallel – look for alternate
interior angles
750
Practice!!
Work on Triangle Congruency Handout.
Use COLOR and arrows to make sure you have
corresponding parts matched up.
FINISH for HOMEWORK!
Debrief
What triangle “shortcuts” guarantee”
two triangles are congruent?
Which two do NOT?
How can you tell if you can make a triangle from
side lengths alone? What must be true?