Chapter 3 Flashcards

1
Q

parallel lines

A

coplanar lines that do not intersect

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2
Q

skew lines

A

non coplanar lines that are not parallel nor intersecting

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3
Q

parallel planes

A

planes that do not intersect

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4
Q

theorem 3-1

A

if 2 parallel lines are cut by a third plane, then the lines of intersection are parallel

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5
Q

transversal

A

line that intersects two or more coplanar lines in unique points

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6
Q

alternate interior angles

A

two nonadjacent interior angles on opposite sides of the transversal

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7
Q

same-side interior angles

A

two interior angles on the same side of the transversal

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8
Q

corresponding angles

A

two angles in corresponding positions relative to the two lines

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9
Q

theorem 3-2

A

if two parallel lines are cut by a transversal, then alternate interior angles are congruent

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10
Q

theorem 3-3

A

if two parallel lines are cut by a transversal, then same-side interior angles are supplementary

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11
Q

theorem 3-4

A

if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also

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12
Q

postulate 11

A

if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel

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13
Q

theorem 3-5

A

if two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel

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14
Q

theorem 3-6

A

if two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel

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15
Q

theorem 3-7

A

in a plane two lines perpendicular to the same line are parallel

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16
Q

theorem 3-8

A

through a point outside a line, there is exactly one line parallel to the given line

17
Q

theorem 3-9

A

through a point outside a line, there is exactly one line perpendicular to the given line

18
Q

theorem 3-10

A

two lines parallel to a third line are parallel to each other

19
Q

scalene triangle

A

no sides congruent

20
Q

isosceles triangle

A

at least two sides congruent

21
Q

equilateral triangle

A

all sides congruent

22
Q

acute

A

three acute angles

23
Q

obtuse

A

one obtuse angle

24
Q

right

A

one right angle

25
equiangular
all angles congruent
26
theorem 3-11
the sum of the measures of the angles of a triangle is 180
27
third angles theorem
if 2 angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent
28
corollary 2
each angle of an equiangular triangle measure 60
29
corollary 3
in a triangle, there can be at most one right angle or obtuse angle
30
corollary 4
the acute angles of a right triangle are complementary
31
theorem 3-12
the measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles
32
polygon
many angles
33
convex polygon
a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon
34
diagonal
segment joining two nonconsecutive vertices
35
theorem 3-13
the sum of the measures of the angles of a convex polygon with n sides is (n-2)180
36
theorem 3-14
the sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360
37
inductive reasoning
- conclusion based on several past observations | - conclusion is probably true, but not necessarily true