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Exam (elaborations)

geometry final exam answer key

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geometry final exam

Final Exam Review -
Solutions

Geometry Matters
(University)

, lOMoARcPSD|10935195




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1RWH
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DSSHDURQWKHH[DP 7KHVHSUREOHPVZHUHVHOHFWHGEHFDXVH WKH\DUHUHSUHVHQWDWLYHRIPDQ\RIWKH
ELJLGHDVZH¶YHFRYHUHGWKXVIDUDQGFDQWKHUHIRUHKHOS\RXLGHQWLI\WRSLFV\RXQHHGWRUHYLHZPRUHRI
,WLVDJRRGLGHDWRUHYLHZROGKRPHZRUNSUREOHPVFODVVH[HUFLVHVDQGSUHYLRXVH[DPVDVZHOO

 )LOOLQWKHEODQNVEHORZZLWKWKHFRUUHFWWHUPLQRORJ\
EDVHGRQWKHGLDJUDPDWULJKW

D $QJOHDDQGDQJOHEDUHFRQJUXHQWEHFDXVHWKH\
DUHBBBBBBBBBBBBBBBBBBBBB
opposite angles
(a.k.a .
vertical angles)
E ,I/DQG0DUHSDUDOOHOWKH3DUDOOHO3RVWXODWHWHOOV
XVWKDWDQJOHEDQGDQJOHFDUHFRQJUXHQWEHFDXVH
WKH\DUHBBBBBBBBBBBBBBBBBBBBB
corresponding angles
F ,I/DQG0DUHSDUDOOHOWKH3DUDOOHO3RVWXODWHWHOOVXVWKDWDQJOHEDQGDQJOHGDUH
FRQJUXHQWEHFDXVHWKH\DUHBBBBBBBBBBBBBBBBBBBBB
alternate interior angles


 /DQG0DUHSDUDOOHOOLQHV'HWHUPLQHWKHXQNQRZQDQJOHV%ULHIO\H[SODLQKRZ\RXIRXQGHDFK
DQJOH




109° =b
= a
71° 109°



64° 116° 109 __

116° 64°
710


WI 45°
=
135°




A and Z are alternate interior angles so 2- = 64° . Using
and fill all the other
opposite supplementary angles ,
we can
we
angles around 2- in .
Using opposite and supplementary angles ,




can fill in all the angles around b. Then 9=1090 ( corresponding
640+710 -1W 180°
angles There's triangle so or w -45 ? This
-


.
now a =
,
,

to 1800-450=135 ?
is supplementary ✗ so ✗ =




Downloaded by Abdra Sree ()

, lOMoARcPSD|10935195




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if
False ! They 'll only be congruent
the two lines are parallel .




 :KDWLVWKHVXPRIWKHLQWHULRUDQJOHVRIWKHLUUHJXODUJRQEHORZ"<RXVKRXOGVXSSRUW\RXU
DQVZHUZLWKDSLFWXUHDQGQRWMXVWXVHDIRUPXOD
We can break the 7- gon up so that its
The
split across
5 triangles .




angles are
the
to 180°, so

angles
in each triangle sum
to 5.1800=9000
the 7- gon sum
in
angles




 )LOOLQWKHEODQNVEHORZZLWKWKHPRVWDFFXUDWHZRUGSRVVLEOH
quadrilateral
D $SRO\JRQZLWKVLGHVLVFDOOHGDBBBBBBBBBBBBB

trapezoid
E $SRO\JRQZLWKVLGHVZLWKDWOHDVWRQHSDLURISDUDOOHOVLGHVLVDBBBBBBBBBBBBBBBB

F $SRO\JRQZLWKVLGHVZLWKWZRSDLUVRISDUDOOHOVLGHVLVDBBBBBBBBBBBBBBBB
parallelogram
G $SRO\JRQZLWKVLGHVWKDWDUHDOOFRQJUXHQWLVDBBBBBBBBBBBBBBBB
rhombus


H $SRO\JRQZLWKVLGHVWKDWKDVDOORILWVDQJOHVHTXDOLVDBBBBBBBBBBBBBBBB
rectangle

equilateral
I $SRO\JRQWKDWKDVDOORILWVVLGHVHTXDOLVFDOOHGD Q BBBBBBBBBBBBBBBBSRO\JRQ

J $SRO\JRQWKDWKDVDOORILWVDQJOHVHTXDOLVFDOOHGD Q BBBBBBBBBBBBBBBBSRO\JRQ
equiangular
K $SRO\JRQWKDWKDVDOORILWVVLGHVHTXDODQGDOORILWVDQJOHVHTXDOLVFDOOHGD Q
BBBBBBBBBBBBBBBBSRO\JRQ
regular




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Written in
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