1. Geometry 14 Nov 2012
WARM UP- 1) sketch and label vertex angle base angles remote interior angles exterior angle adjacent interior angle Find measures of all angles 2) if x = 140⁰. Show work. B C X A

2. objective
Students will explore and apply triangle inequalities and congruency shortcuts. Students will take notes, do a whole class investigation and work problems collaboratively.

3. 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),
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

4. THERE WILL BE NO HOMEWORK ASSIGNED OVER THE THANKSGIVING BREAK!!
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!!

5. 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.)

6. A peek at the interim–
Correct Answers: YOUR TASK: CORRECT FIVE questions! MOST MISSED: 2, 4, 8, 13, 16, 17
1- B
2- D
3- D
4- D
5- C
6- A
7- B
8- A
9- A
10- B
11- C
12- B
13- D
14- B
15-D
16- C
17- B
18- A
19- C
20- D

7. 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!

8. Side-Angle Inequality Conjecture
Term
Conjecture
Examples
Triangle Inequality
The sum of the lengths of any two sides of a triangle is greater than the length of the 3rd side
Side-Angle Inequality Conjecture
In a triangle, if one side is longer than another side, then the angle opposite the longer side is the largest angle.
Triangle Exterior Angle Conjecture
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles

9. Determine whether it is possible for a triangle to have sides measuring……. explain briefly
Arrange the lettered measures in order from greatest to least:

10. 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!)
AAA– SIMILAR but not necessarily congruent!

11. Proving Triangles Congruent

12. The Idea of a Congruence
Two geometric figures with exactly the same size and shape. A C B D E F

13. How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?

14. 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. B A C
AB  DE
BC  EF
AC  DF
 A   D
 B   E
 C   F
ABC   DEF E D F

15. Do you need all six ?
NO !
SSS
SAS
ASA
AAS

16. Triangle congruence shortcuts “included” and “adjacent”
see page 221
“included” and “adjacent”
SSS Congruence shortcut
Side – Side- Side
SAS Congruence shortcut
Side – included Angle - Side

17. Side-Side-Side (SSS)
AB  DE
BC  EF
AC  DF
ABC   DEF B A C E D F

18. Side-Angle-Side (SAS)B E F A C D
AB  DE
A   D
AC  DF
ABC   DEF
included
angle

19. Included Angle
The angle between two sides
 H
 G
 I

20. Included Angle Name the included angle: YE and ES ES and YS YS and YE

21. Angle-Side-Angle (ASA)B E F A C D
A   D
AB  DE
 B   E
ABC   DEF
included
side

22. Included Side
The side between two angles GI GH HI

23. Included Side Name the included side: Y and E E and S S and Y YEES SY

24. Angle-Angle-Side (AAS)B E F A C D
A   D
 B   E
BC  EF
ABC   DEF
Non-included
side

25. There is no such thing as an SSA postulate! NOT necessarily CONGRUENT
Warning: No SSA Postulate
There is no such thing as an SSA postulate! E B F A C D
NOT necessarily CONGRUENT

26. There is no such thing as an AAA postulate! NOT necessarily CONGRUENT
Warning: No AAA Postulate
There is no such thing as an AAA postulate! E B A C F D
NOT necessarily CONGRUENT

27. The Congruence Shortcut Conjectures
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence

28. Chapter 4 Triangles Definition SSS Congruence Shortcut
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
SSA
DOES NOT guarantee congruency
Isosceles ΔABC A B C D

29. Chapter 4 Triangles-- Definition ASA Congruence Shortcut
Term
Definition
Example
ASA
Congruence Shortcut
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.
SAA Congruence Shortcut
If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent
AAA
DOES NOT guarantee congruency

30. Chapter 4 Triangles-- Definition ASA Congruence Shortcut
Term
Definition
Example
ASA
Congruence Shortcut
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.
SAA Congruence Shortcut
If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent
AAA
DOES NOT guarantee congruency

31. and the triangles are congruent by
Chapter 4 Triangles--
Term
Definition
Example
Hypotenuse- Leg
Congruence Shortcut
If an hypotenuse and a leg of two right triangles are congruent, the triangles are congruent.
Proof: if ΔABC and ΔDEF are both right triangles
Then AC2 + CB2 = AB2
and DF2 + FE2 = ED2
if AC = DF and AB = DE
Then BC = EF
and the triangles are congruent by
SSS congruence

32. Study Sheet Write this down!
If two triangles are back to back – they share a common SIDE
“same side”
Study Sheet
Write this down!
If two triangles meet at a vertex– vertical angles are congruent
If two triangles meet at a vertex– and the sides are parallel – look for alternate interior angles

33. Practice!!
Work on Triangle Congruency Handout. Use COLOR and arrows to make sure you have corresponding parts matched up. FINISH for HOMEWORK!

34. 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?