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Chapter 9 and Chapter 11 Review
Chapter 9: Introductory Geometry
9.1 Basic Notions
9.1.1. Vocabulary
9.1.1.1. point – no length, width, or height; only has location
9.1.1.2. line – length, but no width or height
9.1.1.3. plane – length and width, but no height
9.1.1.4. space – the set of all points
9.1.2. linear notions
9.1.2.1. collinear points – points on the same line
9.1.2.2. between-ness – three distinct points on a line – one point is
between the other two
9.1.2.3. line segment – a subset of a line containing two points and all of the
points between those two points
9.1.2.4. ray – subset of a line containing one point and all of the points on
one side of that point
9.1.3. planar notions
9.1.3.1. coplanar – points in the same plane
9.1.3.2. noncoplanar – not in the same plane
9.1.3.3. coplanar lines – lines in the same plane
9.1.3.4. skew lines – noncoplanar lines
9.1.3.5. intersecting lines – two coplanar lines that have exactly one point in
common
9.1.3.6. concurrent lines – lines that contain the same point
9.1.3.7. parallel lines – two distinct coplanar lines with no points in common
9.1.3.8. Now Try This 9-1: p. 500
9.1.3.9. properties of points, lines, and planes
 there is exactly one line that contains any two distinct points
 if two points lie in a plane, then the line containing the points lies
in the plane
 if two distinct planes intersect, then their intersection is a line
 there is exactly one plane that contains any three distinct
noncollinear (not all on the same line) points
 a line and a point not on the line determine a plane
 two parallel lines determine a plane
 two intersecting lines determine a plane
9.1.3.10. Now Try This 9-2: p. 501
9.1.3.11. Now Try This 9-3: p. 502
9.1.4. Other Planar Notions
9.1.4.1. half-plane – two planes intersect at exactly one line; that line
divides each plane into halves see fig 9-2 p. 503
9.1.4.2. a line and plane are related in one of 3 ways: see fig. 9-3 p. 503
9.1.4.2.1. line and plane no points in common, the line is parallel to the
plane
9.1.4.2.2. If two points on the line are in the plane, then the entire line is in
the plane
9.1.4.2.3. If a line intersects a plane, but is not contained in the plane, it
intersects the plane at exactly one point
9.1.5. angles
9.1.5.1. angle – formed by two rays with a common endpoint
9.1.5.2. side – formed by a ray
9.1.5.3. vertex – the common endpoint
9.1.5.4. adjacent angles – share a common side and vertex, but do not
overlap interiors
9.1.6. angle measurement
9.1.6.1. degrees – 360 form a circle
9.1.6.2. protractor – measuring device or ruler to measure degrees
9.1.6.3. minutes – subdivision of a degree – 60 minutes = 1 degree
9.1.6.4. seconds – subdivision of a minute – 60 seconds = 1 minute
9.1.6.5. radian – in calculus, trigonometry, and science used as angle
measure: 1 radian  57.296o
9.1.6.6. grad – sometimes used in civil engineering: 1 grad = 0.9o
9.1.6.7. Now Try This 9-4: p. 504
9.1.7. types of angles
9.1.7.1. acute <90o
9.1.7.2. right = 90o
9.1.7.3. 90o < obtuse < 180o
9.1.7.4. straight angle = 180o
9.1.8. Perpendicular lines
9.1.8.1. Perpendicular lines – intersect to form right angles
9.1.9. a line perpendicular to a plane
9.1.9.1. a line that is perpendicular to every line in the plane
9.1.9.2. Now Try This 9-5: p. 509
9.1.9.3. Theorem 9-1: A line perpendicular to two distinct lines in the plane
through its intersection with the plane is perpendicular with the plane
9.1.10. Ongoing assessment: p. 509: 1a, 2aceg, 3ac, 4ace, 5, 7ac, 10a(i, iii)c,
12ac, 13a, 16a, 17ac