Geometry 4.2 Triangle Sum Theorem & Exterior Angles...

Geometry4.2TriangleSumTheorem&ExteriorAnglesTheorem

Mr.Deyo

Bytheendoftheperiod,studentswillapplytheoremsabouttheinteriorandexterioranglesoftriangles.

Studentswilldemonstratethisbycompletingagraphicorganizerandsolvingproblemsinapairactivity.

Learning Target

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1.  How are the two pictures similar? 2.  How are they different? 3.  How can these two pictures be related to math?

1)  Supplementary

2)  TriangleSum

3)  RemoteInteriorAngle

4)  ExteriorAngle

Vocabulary

DAY 3 and/or DAY 4 1. Review the word

♦ Friendly Definition ♦ Physical Representation

2. Show how the word works ♦ Synonyms/antonym ♦ Word Problems ♦ Related words/phrases ♦ Example/non-example

Friendly Definition Sketch

Wordwork Sentence

DAY 2 1. Review word

♦ Friendly Definition ♦ Physical Representation

2. Draw a sketch

DAY 5 1. Review the word

♦ Friendly definition ♦ Physical Representation

3. Write a sentence  at least 2 rich words (1 action)  correct spelling  correct punctuation  correct subject/predicate agreement  clear and clean writing

DAY 1 1.  Use Visuals

2.  Introduce the word ♦ Friendly Definition ♦ Physical Representation

3.  Use Cognates

4.  Write friendly definition

5.  Physical Representation

WordList1.  2.  3.  4. 

Notes:

A‐BProblemAnotes:

Find m∠K and m∠J.

A‐BProblemACheck:

Find m∠K and m∠J.

∠K ≅ ∠J m∠K = m∠J

4y2 = 6y2 – 40

–2y2 = –40

y2 = 20

So m∠K = 4y2 = 4(20) = 80°. Since m∠J = m∠K, m∠J = 80°.

Third ∠s Thm.

Def. of ≅ ∠s.

Substitute 4y2 for m∠K and 6y2 – 40 for m∠J.

Subtract 6y2 from both sides.

Divide both sides by -2.

A‐BProblemBSOLVE!!

Find m∠P and m∠T.

A‐BProblemBCheck!!

Find m∠P and m∠T.

∠P ≅ ∠T m∠P = m∠T

2x2 = 4x2 – 32

–2x2 = –32

x2 = 16

So m∠P = 2x2 = 2(16) = 32°. Since m∠P = m∠T, m∠T = 32°.

Third ∠s Thm.

Def. of ≅ ∠s.

Substitute 2x2 for m∠P and 4x2 – 32 for m∠T.

Subtract 4x2 from both sides.

Divide both sides by -2.

StormCheck(Think,Write,Discuss,Report)

WhatistheTriangleSumTheorem?Thetrianglesumtheoremstatesthat_________

_______________________________________.

WhatistheThirdAngleTheorem?

TheThirdAngleTheoremstatesthat_________

_______________________________________

_______________________________________.

Notes:

InteriorExterior

A‐BProblemAnotes:

Find m∠B.

A‐BProblemACheck:

Find m∠B.

m∠A + m∠B = m∠BCD Ext. ∠ Thm.

15 + 2x + 3 = 5x – 60 Substitute 15 for m∠A, 2x + 3 for m∠B, and 5x – 60 for m∠BCD.

2x + 18 = 5x – 60 Simplify.

78 = 3x Subtract 2x and add 60 to both sides.

26 = x Divide by 3.

m∠B = 2x + 3 = 2(26) + 3 = 55°

A‐BProblemBSOLVE!!

Findm∠ABD.

A‐BProblemBCheck!!

Findm∠ABD.

m∠ABD=m∠BDC+m∠DCB Ext.AngleTheorem2x+16=58+x+12 Substitution2x+16=x+70 CombineLikeTermsx+16=70 Sub.Pr.OfEqualityx=54 Sub.Pr.OfEquality

m∠ABD=2(54)+16m∠ABD=108+16m∠ABD=124°

StormCheck(Think,Write,Discuss,Report)

WhatistheExternalAngleTheorem?

TheExternalAngleTheoremstatesthat______

_______________________________________

_______________________________________

_______________________________________.

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

Vocabulary Review 1)  Supplementary

2)  TriangleSum

3)  RemoteInteriorAngle

4)  ExteriorAngle

Learning Target

Bytheendoftheperiod,studentswillapplytheoremsabouttheinteriorandexterioranglesoftriangles.

Studentswilldemonstratethisbycompletingagraphicorganizerandsolvingproblemsinapairactivity.

Ticket OUT.

ThediagramisamapshowingJohn'shouse,Kay'shouse,and

thegrocerystore.Whatistheanglethetwohousesmakewiththestore?

Ticket OUT.

ThediagramisamapshowingJohn'shouse,Kay'shouse,and

thegrocerystore.Whatistheanglethetwohousesmakewiththestore?

30°