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 (neither parallel nor intersecting)

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3
Q

theorem about parallel planes

A

If two parallel planes are cut by a third plane, then the lines of intersection are parallel

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4
Q

transversal

A

a line that intersect two or more coplanar lines in different points

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5
Q

interior angles

A

inside the two lines cut by the transversal

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6
Q

exteriors angles

A

outside the two lines cut by the transversal

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7
Q

corresponding angles postulate

A

If 2 parallel lines are cut by a transversal, then corresponding angles are congruent

Converse:
If 2 lines are cut by a transversal and corresponding angles are congruent, then the two lines are parallel

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8
Q

postulate about alternate interior angles

A

If 2 parallel lines are cut by a transversal, then alternate interior angles are congruent

converse:
If 2 lines are cut by a transversal and alternate interior angles are congruent, then the two lines are parallel

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9
Q

theorem about same side interior angles

A

If 2 parallel lines are cut by a transversal, then same-side interior angles are supplementary

converse:
If 2 lines are cut by a transversal and same side interior angles are supplementary, then the two lines are parallel

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10
Q

theorem about perpendicular lines

A

If a transversal is perpendicular to one of the parallel lines, then it is also perpendicular to the other one.

converse:
If 2 lines are perpendicular to the same line, then the two lines are parallel.

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11
Q

theorems (3)

A

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

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

Two lines parallel to a third line are parallel to each other.

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12
Q

classification of triangles by sides

A

equilateral: 3 congruent sides
isosceles: at least 2 congruent sides
scalene: no congruent sides

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13
Q

classification of triangles by angles

A

acute: 3 acute angles
equiangular: 3 congruent angles (60 degrees)
right: 1 right angle
obtuse: 1 obtuse angle

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14
Q

triangle angle-sum theorem

A

The sum of the three angles of a triangle is 180

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15
Q

third angle theorem

A

If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent

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16
Q

angles of equilateral triangles

A

equilateral triangles are also equiangular, so each angle of an equilateral triangle is 60 degrees.

17
Q

exterior angle theorem

A

the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

18
Q

consecutive vertices

A

2 vertices that are endpoints on the same side

19
Q

diagonal

A

a segment that join 2 non consecutive vertices of a polygon

20
Q

convex polygons

A

vertices are outside the shape

21
Q

concave (nonconvex) polygons

A

at least 1 vertex on the inside

22
Q

regular polygon

A

equilateral and equiangular

23
Q

polygon angle sum formula

A

n = number of sides
(n-2) x 180

24
Q

for any polygon (flow)

A

sum of interior angles: (n-2) x180
sum of exterior angles: 360

25
Q

for regular polygons (flow)

A

n (number of sides) = 360/measure of exterior angle