Download Lines and angles – lines - Berkeley Primary School

Lines and angles – lines
681&$?1$.7"%%(<>$7(&1%$?1$*%1$#1;=%$%*.8$"%$+";"7717A$+1;+1&'(.*7";A$J1;-."7$"&'$80;(K0&#"75
Knowing these terms makes it easier for us to understand and work with shapes.
1
='44';#-/"#$),-+(25'),#.)*#>44#$)#-/"#0$,,$)6#$)%'+0.5')<
"
a L ook at the horizontal line in the box below. Horizontal lines lie !!"#$$$!$%#"&'(&)$*+$,-./$0&1$20345$
61$."77$#81$7(&1$9:$"%$(#$%#";#%$"#$9$"&'$1&'%$"#$:5
b Draw a 5 cm ?"+52.4$7(&1$*+$<;0=$+0(&#$95$68"#$/(&'$0<$"&)71$(%$<0;=1'$2>$#81
#?0$7(&1%$"#$9@$$
right angle
______________
c$ 6
$ 81&$#?0$7(&1%$=11#$(&$%*.8$"&$"&)71A$?1$%">$#8"#$#81>B;1$perpendicular to each
yes
0#81;5$C;"?$"&0#81;$D$.=$7(&1$*+$<;0=$:5$E%$#8(%$7(&1$+1;+1&'(.*7";$#0$7(&1$9:$"%$?177@$ ______________
parallel
______________
d$ $F0?$700/$"#$7(&1%$9G$"&'$:C5$9;1$#81>$+1;+1&'(.*7";$0;$+";"7717$#0$1".8$0#81;@$
e$ E$<$>0*$%"('$parallelA$>0*B'$21$;()8#5$H";"7717$7(&1%$";1$"7?">%$#81$%"=1$'(%#"&.1$"?">$<;0=$1".8$0#81;$
at any point and can never meet.
f$ C;"?$"$7(&1$#8"#$(%$+";"7717$#0$7(&1$9:$2>$I0(&(&)$GC5$
6 Curves can also be parallel. Draw 2 parallel curves in the shape.
2
C
D
A
B
!""#$%#&'(#()*"+,-.)*#-/","#-"+0,#1&#2'034"5)6#-/$,#7($28#-",-9#:+.;<
a 2 parallel lines
b 2
lines perpendicular to each other
c a horizontal line
Geometry
Copyright © 3P Learning
d$ "$J1;-."7$7(&1
F
1
SERIES
TOPIC
1
Lines and angles – lines
J/.-#$,#.)#.)64"K
Look at where these two lines meet. The angle is the amount of space 21#?11&$?81;1$#81>$I0(&5$E#B%$"7%0$#81$"=0*&#$0<$#*;&$21#?11&$#81=5
E<$?1$(=")(&1$#8"#$#81%1$#?0$7(&1%$";1$I0(&1'$
"#$#81(;$=11-&)$+0(&#A$?1$.0*7'$;0#"#1$#81$
7(&1%$";0*&'$#8(%$+0(&#5$L81>B77$%#">$I0(&1'$
but the amount of turn will change.
We measure angles using degrees – the symbol for this is °. We use a protractor as our measuring tool.
@#2$+24"#$,#.#%(44#-(+)#.)*#$,#ABCD9#E/$)8#'%#$-#.,#.#24'28# F#%+'0#GH<CC#+'()*#-'#GH<CC9#I'3&#-/$,#3.6"#.)*#-/")#
2(-#'(-#-/"#2$+24"#1"4';#.)*#-+&#-/"#%'44';$)6<
copy
a Fold the circle in half. How many degrees are in a half circle? 180 P
___________________
b F old it in half again. You now have a quarter circle. How many degrees are in a quarter of a circle? 90 P
___________________
c Fold it in half once more. You have an eighth of a circle. How many degrees
are in one eighth of a circle? 45 P
___________________
O
MN
C
MN
O
C
MNOC
3
MNOC
MNOC
O
MN
C
MN
O
C
MNOC
2
F
1
SERIES
TOPIC
Geometry
Copyright © 3P Learning
Lines and angles – introducing angles
681&$"&$"&)71$(%$71%%$#8"&$"$Q*";#1;$#*;&$0<$RST$?1$%">$(#B%$acute.
681&$(#B%$13".#7>$RST$?1$%">$(#B%$"$+$6/- angle. 681&$(#B%$21#?11&$RST$"&'$UVST$?1$%">$(#B%$obtuse.
681&$(#B%$13".#7>$UVST$?1$%">$(#B%$"$,-+.$6/- angle.
UVST
681&$(#B%$=0;1$#8"&$UVST$?1$%">$(#B%$"$+"O"L angle.
We use an arc WXST
.
M.1"4#".2/#'%#-/","#.)64",#.,#+$6/-N#.2(-"#'+#'1-(,"<
a
b
acute
c
right
angle
d
angle
f
acute
angle
acute
angle
angle
J.44&#-/"#;'+8#"L3"+$")2"#1'&#0.*"#,'0"#0$,-.8",#4.1"44$)6#-/","#.)64",9#I'++"2-#.)&#0$,-.8",#&'(#,""9
a
b
c
reflex
obtuse
3
obtuse
angle
e
obtuse
2
ST YZST
$#0$%80?$?81;1$?1B;1$=1"%*;(&)5
6(#8$;()8#$"&)71%A$?1$*%1$"$%Q*";1$%>=207$7(/1$#8(%$
1
RST
d
acute
straight
angle
;1!13
angle
b
acute
c
right
angle
acute
angle
Remember to #0.+8#&'(+#.)64", #;$-/# or !
:+.;#-/"#'-/"+#4$)"#-'#2+".-"#.)#.)64"#-/.-#$,<#
a
obtuse
obtuse
Geometry
Copyright © 3P Learning
F
1
SERIES
TOPIC
3
Lines and angles – measuring angles
[0=1-=1%$?1$&11'$#0$21$=0;1$+;1.(%1$?81&$&"=(&)$
"&)71%A$(&%#1"'$0<$I*%#$*%(&)$#1;=%$%*.8$"%$".*#1$0;$
obtuse. This is where a protractor comes in handy. To measure an angle using a protractor we:
#$$$\#$#81$2"%17(&1$0<$#81$+;0#;".#0;$#0$0&1$7(&1$
0<$#81$"&)71A$7(&(&)$*+$#81$.1&#;1$+0(&#$0<$ the protractor with the vertex of the angle
# look where the other line intersects the baseline
&*=21;%A$="/(&)$%*;1$?1$;1"'$;0*&'$<;0=$ST5
1
DST
This is an angle 0<$DST
ST
centre point
P,"#.#3+'-+.2-'+#-'#0".,(+"#.44#'%#-/","#0.+8"*#.)64",9#J+$-"#-/"#.),;"+,#$)#-/"#.)64",<
80 °
____
80 °
____
100 °
____
100 °
____
120 °
____
120 °
____
90 °
____
90 °
____
90 °
____
90 °
____
75 °
___
115 °
____
120 °
____
120 °
____
105 °
____
120 °
____
4
F
1
SERIES
TOPIC
120 °
____
70 °
____
Geometry
Copyright © 3P Learning
225P
130 °
____
Lines and angles – measuring angles
2
P,"#.#3+'-+.2-'+#-'#2'034"-"#-/","#.)64",9#T)"#4$)"#$,#*+.;)#%'+#&'(9#U'(#)""*#-'#0".,(+"#.)*#*+.;# -/"#'-/"+#4$)"9#:+.;#$-#.1'(-#-/"#,.0"#4")6-/#.,#-/"#'-/"+#4$)"9#Q.+8#-/"#.)64",#;$-/#-/"#0".,(+"0")-,9
a
b
]DT
d
c
ZST
Line the middle of your 3+'-+.2-'+#(3#;$-/#-/"#*'-#
.-#-/"#")*#'%#-/"#4$)"9
e
UUST
RST
UST
When we talk about measuring angles we usually mean the interior angle. We can also measure the exterior angle – the one on the outside. 3
I.)#&'(#-/$)8#'%#.#;.&#-'#0".,(+"#-/"#"L-"+$'+#.)64",#'%#-/","#H#>6(+",K#Q.&1"#.#%(44#RABCDS#3+'-+.2-'+#
;'(4*#/"43#'+#$,#-/"+"#.)'-/"+#;.&#-'#2.42(4.-"#-/.-#'(-,$*"#.)64"#;$-/'(-#.2-(.44&#0".,(+$)6#$-K# J/.-#"4,"#2'(4*#&'(#0".,(+"K
270 °
______
V';#0.)&#*"6+"",#
$)#.#%(44#-(+)K#V';#
2'(4*#-/$,#/"43#0"K
35°
325 °
______
Geometry
Copyright © 3P Learning
F
1
SERIES
TOPIC
5