Geometry Diff Chapter 3 Test Review Answers
1.
Alternate Exterior Angles
2.
Consecutive Interior Angles
3.
Alternate Interior Angles
4.
m=
−6 −1 −7
, therefore the slope is undefined
=
8 −8
0
5.
m=
0 − 6 −6
3
=
=−
4 −0 4
2
6.
m=
3−3
0
=
=0
6 − ( −6) 12
7.
m=
1 − 4 −3
=
= −1
8 −5 3
8.
m∠9 = 84° , because it is a consecutive interior angle with ∠8 , and ∠8 is a vertical angle with ∠2 .
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€
€ 9.
m∠11 = 138° , because it is a linear pair angle with ∠12 .
€
10.
€ with ∠12
€ .
m∠6 = 42° , because it is an alternate interior angle
€
11.
€ exterior angles, then
Because the two angles marked are alternate
x − 8 = 120
€
x = 128
13.
For the line y = 2x −17 , m = 2 , then the ⊥ m = − 12 , giving equation of perpendicular line as
€
€
y −1 = − 12 ( x − ( −8))
€
y −1 = − 12 x − 4
€
€
y = − 12 x − 3
€
y − 7 = 4 ( x − 0)
€ 14. For the line y = 4 x −19 , m = 4 , then the || m = 4 , giving equation of parallel line as y − 7 = 4 x − 0
y = 4x + 7
15.
2
− 23 , then the ⊥ m = 23 , giving equation of perpendicular line as
For
€ the line y =€− 3 x −11, m = €
y − 3 = 23 ( x − ( −12))
y −3=
€y =
€
3 x +18
2
3 x + 21
2
€
€
€
16.
For the line y = x −11, use the point (0, -11) and m = 1, then the ⊥ m = −1, giving equation of
y − ( −11) = −1( x − 0)
perpendicular line as
y +11 = −x − 0 .
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€
y = −x −11
x − 7 = −x −11
y = x −7
The intersection of the lines y = x − 7 and y = −x −11 is 2x = −4
and y = ( −2) − 7 . The distance
x = −2
y = −9
€
from (0, -11) to (-2, -9) is d =
€
17.
2
(−2 − 0) 2 + ( −9 − ( −11)) = ( −2) 2 + (2) 2 = 8 ≈ 2.828 .
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For the line y = −2x +1, use the point (0, 1) and m = −2 , then the ⊥ m = 12 , giving equation of
€
y −1 = 12 ( x − 0)
perpendicular line as y −1 =
€
y=
1 x −0 .
2
€
1 x +1
2
€
The intersection of the lines y = −2x +16 and y = 12 x +1 is
−2x +16 = 12 x +1
− 25 x = −15
€
x =6
2
18.
2
2
y = −2x +16
and y = −2(6) +16 . The
y=4
2
distance from (0, 1) to (6, 4) is d = (6 − 0) + ( 4 −1) = (6) + ( 3) = 45 ≈ 6.708 .
€
€
€ on the same plane.
€ intersect and are not
D, because the lines containing CD and VZ will never
€
4 x +11+ 8x +1 = 180
12x +12 = 180
€ marked€are consecutive interior angles, then
19. Because the two angles
.
12x = 168
x = 14
20.
The slope between the point (-4, 2) and (3, -5) is m =
y − 2 = −1( x − ( −4 ))
those points as y − 2 = −x − 4
.
y = −x − 2
−5 − 2
−7
=
= −1 , giving the equation between
3 − ( −4 ) 7
€
€
y − 2 = 1( x −1)
Then the ⊥ m = 1 and the perpendicular line through the point (1, 2) is y − 2 = x −1 .
€
y = x +1
y = x +1
−x − 2 = x +1
€
The intersection of the lines y = −x − 2 and y = x +1 is −2x = 3
and y = − 23 +1.
€
x = − 23
y = − 12
(
)
The distance from €
(1, 2) to − 23 , −€12 is d =
2
(− 23 −1) + (− 12 − 2)
€
€
€
€
2
=
2
(− 25 ) + (− 25 )
2
=
25
2
≈ 3.536 .
21.
The slope between the point (6, 5) and (2, 3) is m =
y − 5 = 12 ( x − 6)
points as y − 5 = 12 x − 3 .
3 − 5 −2 1
=
= , giving the equation between those
2 − 6 −4 2
€
y = 12 x + 2
y − 6 = −2( x − 2)
Then the ⊥ m = −2 and the perpendicular line through the point (2, 6) is y − 6 = −2x + 4 .
y = −2x +10
€
€
The intersection of the lines y = 12 x + 2 and y = −2x +10 is
(
)
, 18
The distance from (2, 6) to 16
is d =
5
5€
€
22.
€
€
1
2
2
x + 2 = −2x +10
€
j || k by the Corresponding Angles Converse Postulate.
23.
€
No lines are parallel because €
there is on common transversal.
24.
p || q by the Alternate Exterior Angles Converse Theorem.
( )
5
€2 x = 8
x = 16
5
(165 − 2) + (185 − 6)
2
=
y = −2x +10
and y = −2 16
+10
5
y = − 32
+ 50
= 18
5
5
5
2
( 65 ) + (− 125 )
€
2
= 180
≈ 2.683 .
25
.