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°