sson 24 angles in triangles - mr. l's...
TRANSCRIPT
LESSON
132 Domain 4: Geometry
Dup
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ing
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of t
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24 Angles in Triangles
UNDERSTAND Atrianglehas3sidesand3interior angles .Ifonesideofatriangleisextended,anexterior angleisformed .
Thesumofthemeasuresoftheinterioranglesinanytriangleis180° .Thisdiagramcanbeusedtoshowthatthisistruefortheshadedtriangle .Inthediagram,linel||linemandtheyarecutbytwotransversals,linesnandp .
n p
l
m
54 2
1 3
Adjacentangles4,2,and5formastraightline .
m/41m/21m/55180°
Lookathowparallellineslandmarecutbytransversallinesnandp .
n p
l
m
54 2
1 3
Whenlinencutsparallellineslandm,itformsalternateinteriorangles5and3 .
Alternateinterioranglesarecongruent,som/55m/3 .
Whenlinepcutsparallellineslandm,itformsalternateinteriorangles4and1 .
Alternateinterioranglesarecongruent,som/45m/1 .
m/45m/1andm/55m/3 .Substitutem/1form/4andm/3form/5intheequationfromabove:m/41m/21m/55180° .
m/11m/21m/35180°
exteriorangle
interiorangle
Connect
Lesson 24: Angles in Triangles 133
Dup
licat
ing
any
part
of t
his
book
is p
rohi
bite
d by
law
.
Findthevalueofx .
x°a°40°
79°
Whatdoesxrepresent?
Itrepresentsthedegreemeasureofanexteriorangleofthetriangle .
Usethefactthatthe61°interiorangleanditsexterioranglearesupplementarytofindthevalueofx .
61°1x°5180°
x°5119°
▸x5119
3
1
First,finda°,themeasureofthethirdinteriorangleofthetriangle .
Thesumofthemeasuresoftheinterioranglesofatriangleis180° .
40°179°1a°5180°
119°1a°5180°
a°561°
2
Istheexteriorangleintheexampletheonlyexterioranglethatcanbedrawnforthistriangle?Ifnot,drawtwoothersandlabeltheirmeasuresy°andz° .
x°a°40°
79°
MODEl
Practice
134 Domain 4: Geometry
Dup
licat
ing
any
part
of t
his
book
is p
rohi
bite
d by
law
.
Write an equation that could be used to find the value of x for each triangle.
1.
x°60°
70°2.
61°
x°
REMEMBER A right angle is 90°.
3.
110° 38°
x°
State whether or not it is possible to draw a triangle with the given interior angle measures.
4. 45°,55°,80° 5. 30°,60°,100° 6. 12°,84°,84°
Find the value of z for each triangle. Show your work.
7.
60°
48°
z°
8.
42°
34°
z°
9.
40°z°
Find the value of x for each triangle. Show your work.
10.
x°28°
32°
11.
x°
30° 82°
Lesson 24: Angles in Triangles 135
Dup
licat
ing
any
part
of t
his
book
is p
rohi
bite
d by
law
.
12.
x°
(2x)°13.
x°110°
41°
Use the diagram below for questions 14–15.
41 3
2
14. Whyisthisstatementtrue?
m/11m/21m/35180°
15. Whyisthisstatementtrue?
m/31m/45180°
Solve.
16. EXPLAIN Iftwotriangleshavethreepairsofcorrespondinganglesthatarecongruent,thetrianglesmustbesimilar .WouldtheinformationgiveninthediagrambelowbesufficienttoallowyoutoprovethatnABCandnDEFaresimilar?Explain .
A C D F
EB
60° 60°40° 40°
17. CONCLUDE Thetriangleonthelefthasinteriorangles1,2,and3 .
1 13
2
23
Martacopiedthistriangle3times,rotatedthosetriangles,andplacedthemtogethersothatangles1,2,and3werealigned .Whatdoesthisallowyoutoconcludeabouttheinterioranglemeasuresofatriangle?Explain .