MN O P M’N’ O’ P’ SAME PLANE R D k.
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Transcript of MN O P M’N’ O’ P’ SAME PLANE R D k.
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M N
OP
M’ N’
O’P’
ACDERule2
1 :
2
104 x
DE
52 xDE
SAME PLANE
221 xx
xm
22
37
mx
221 yy
ym
12
31
my
4,3)2,5( T )2,2(
R
D
k
2 Triple ,4,53 )1
Triple ,15,178 )2
,24,258 )3 222 25248 62557664
625640
80
The diagonals of a rhombus bisects the angles
Consecutive angles of a rhombus are supplementary
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1DBCm
40DBCm
5 4
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2
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2
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bxy 2
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b )2(2
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b 33b6
C
B
A
45
55 80
Longest
Shortest
12
15
BhV hrV 21562 V540V
T F^ FT F FT F FT F T
126 yx
126 xy
26
1 xy
4)2(3 yx
463 yx
4 4 yx 23yx 23
221
221 )()( yyxxd
22 ))6(4()35( d22 )10()8( d
164d414 d
412d
x
5x
5
6
6 x
x
66)5( xx
3652 xx
03652 xx
049 xx
04 09 xx
4 9 xxReject
)2,3( )3,2(90R 4D
)12,8(
x
152 x55 x
15255 xxx15355 xx
1552 x102 x5x
152 x15)5(2
1510 25
m
P
60 120
12060180
302
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AC
B
x
y
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C’A’
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)2,2(
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180)25( S540S
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540angle Int. M.
108angle Int. M.
5
360angle Ext. M.
72angle Ext. M.
x xxx98272 x
272 xx 236
x26
26CE
462 xy462 xy
23 xy3m
3
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4x
X
X
X
:Solutions 1,6,3,2,5,2
Statement Reason
1. Given
anglesright are E and B 4. 4. Perpendicular segments form right angles
BEAB 1.2. Given BEDE 2.
DEFABC ~ 9. AAAA .9
ECABFD 3. 3. Given
5. EB 5. All right angles are congruent
pairlinear a form and pairlinear a form and 6.
ACBECADFEBFD
6. Two adjacent angles that form a
straight line are a linear pair
arysupplement are and arysupplement are and 7.
ACBECADFEBFD
7. Linear pairs are supplementary
ACBDFE 8. 8. Supplements of congruent angles are congruent.
3x
20
16
22 x
36
22
3
36
16
x
x
)3(36)22(16 xx
108363232 xx
108432 x
x4140 x35
3xAC
335 AC32AC
x
y
A
M
T
H
run
risem
05
0ATm
3
4THm
5AMd
4
3
5
tripleean Pythagor5,4,3
5ATd
5THd tripleean Pythagor5,4,3
5HMd
Since all four sides are congruent, quadrilateral MATH is a rhombus.
Since the slopes of consecutive sides are not negative reciprocals, they are not perpendicular and do not form a right angle.
Therefore, MATH is not a square.
