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

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

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!!

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.)

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

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!

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

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

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. A C B D E F

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

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

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

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

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

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

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

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

Included Side The side between two angles GI GH HI

Included Side Name the included side: Y and E E and S S and Y YE ES SY

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

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

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

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

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

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

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

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

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

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?