Download 9.1-9.5 Review Answer Key

Sections 9.1­9.5 Review
6th Grade A&E
Name ______________________________
Date ___________________ Per. _____
*Vocabulary ­ know what these terms mean and how to label (where appropriate)
Point ­ position in space with no dimension
Line ­ one dimensional figure that continues without an end in opposite directions
Plane ­ flat surface with no thickness that continues without end in all directions
Ray ­ part of a line with one endpoint and continues with no end in one direction
Segment ­ part of a line with 2 endpoints
Parallel ­ two or more lines on the same plane that never intersect
Skew ­ two or more lines not on the same plane that never intersect
Perpendicular ­ lines that intersect to form all right angles
Angle ­ two rays with a common endpoint
Vertex ­ the point at which 2 rays meet to form an angle
Acute angle ­ measures between 0o and 90o
Right angle ­ measures exactly 90o
Obtuse angle ­ measures between 90o and 180o
Straight angle ­ measures exactly 180o
Reflex angle ­ measures between 180o and 360o
Supplementary ­ two angles whose sum is exactly 180o
Complementary ­ two angles whose sum is exactly 90o
Vertical angles ­ opposing angles in the intersection of two lines [congruent]
Adjacent angles ­ angles that share a common ray [supplementary when formed by 2 lines]
Transversal ­ a line that crosses the paths of 2 or more parallel lines … creates the following:
Corresponding angles ­ play the same role in their respective intersections [congruent]
Alternate Interior angles ­ angles inside the parallel lines, different sides of the transversal
Alternate Exterior angles ­ angles outside the parallel lines, different sides of the transversal
Triangle (Equilateral, Isosceles, Scalene … Acute, Right, Obtuse) ­ see next page
Quadrilateral (Trapezoid, Parallelogram, Rectangle, Rhombus, Square) see next page
Polygon (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon)
Diagonal ­ segment in a polygon connecting a vertex to a vertex that is not a side Angle Sum ­ sum of the interior angles in a polygon S = 180 (n ­ 2)
Circle (center, radius, diameter, chord, arc, central angle) see next page
Polygon ­ closed plane figure that is a set of segments that do not cross.
Concave polygon ­ contains at least one reflex angle
Convex polygon ­ contains no reflex angles
Regular ­ equilateral and equiangular (its sides and angles are congruent)
Polygon Classifications (number of sides, angles, vertices)
Triangle (3), Quadrilateral (4), Pentagon (5), Hexagon (6), Heptagon (7), Octagon (8), Nonagon (9), Decagon (10)
Classifications for a Triangle (2 categories)
By side/angle congruencies …
Equilateral / Equiangular ­ all sides / angles congruent
Isosceles ­ at least 2 sides / angles congruent
Scalene ­ no sides / angles congruent
By angle measures …
Acute ­ all three angles are acute
Right ­ one right angle, two acute angles
Obtuse ­ one obtuse angle, two acute angles
Special Quadrilaterals
Trapezoid ­ has one pair of parallel sides
Parallelogram ­ has 2 pairs of parallel and congruent opposite sides; opposite angles congruent
Rectangle ­ equiangular parallelogram
Rhombus ­ equilateral parallelogram
Square ­ regular parallelogram (equilateral and equiangular)
Parts of a Circle
Center ­ point in which all points on a circle are the same distance from
Radius ­ segment connecting the center to a point on the circle (half the diameter)
Chord ­ segment connecting two points on a circle
Diameter ­ special chord that passes through the center (twice the radius)
Central Angle ­ angle whose vertex is the center of a circle
Arc ­ part of a circle
line p is parallel to line q
line p is perpendicular to
<ABI
<CBI
<LMG
<NMG
(more possible)
<JCE
<DCE
(more possible)
<HIB
<JIB
(more possible)
<BCD
<CJI
(more possible)
<JKE
<KEG
<BCD
<KJ_
(more possible)
(point missing my mistake)
FE
"measure of"
<ABI is a geometric part, not a number
a) m<BIJ = 58o since it is alternate interior to the given 58o angle
b) m<CJI = 60o since it corresponds to the supplement of the given 120o angle
c) m<GMN = 49o since it is complementary to the given 41o angle
d) m<MGN = 41o since <MGN, <GMN and the given right angle form a triangle
S = 180 (14 - 2)
S = 180 (12) = 2,160o
The angle sum is 2,160o
2700 = 180 (n - 2)
180 180
15 = n -2
D = 10 (10 - 3)
2
D = 70 / 2 = 35
A = 2160 / 14
A ≈ 154.29
Each angle measures ≈ 154.29o
n = 17
The polygon has 17 vertices.
A decagon has 35 diagonals.
180 (n - 2) = (180) (3) (7 - 2)
180 (n - 2) = (180) (15)
n -2 = 15
n = 17
The polygon has 17 sides.
Let n = number of sides
in missing polygon
Every minute ...
minute hand moves 6o
hour hand moves 1/2o
Let n = the complement
n + 17 = missing angle
Let n = the supplement
2n - 8 = missing angle
Let
b = m <B
b + 12 = m < C
2(b + 12) = m < A
39 (6) = 234o
4 o'clock = 120o
+ 39 (1/2) = 19.5o
n + n + 17 = 90
2n + 17 = 90
- 17 -17
2n = 73
n + 2n - 8 = 180
3n -8 = 180
+8 +8
3n = 188
n = 62 2/3
234o - (120o + 19.5o)
234 - (139.5) = 94.5
The angle measure is 94.5o.
n = 36.5
n + 17 = 53.5
The missing angle is 53.5o.
2(62 2/3 ) - 8 = 117 1/3
The missing angle is 117 1/3o.
b + b + 12 + 2b + 24 = 180
4b + 36 = 180
-36 -36
4b = 144
b = 36
b + 12 = 48
2(b+12) = 96
36o = m <B
48o = m < C
96o = m < A
109o
109o
x + 2(x + 14) = 180
x + 2x + 28 = 180
3x + 28 = 180
-28
-28
3x = 152
3
3
x = 50 2/3o
x + 109 + 38 = 180
x + 147 = 180
-147 -147
x = 33o
155o 25o
25o
<AGF, <AGB
see picture
HI
10 cm
≈ 43%
Arc AHB is formed by the central angle <AGB which is
155o. 155/360 ≈ 43% of the way around the circle.
C
D
E
A,F
A,F
B