Geometry - Parallel Lines And Planes

Front 1

Parallel lines

Back 1

Coplanar lines that do not intersect

Front 2

Skew Lines

Back 2

noncoplanar lines, they are not parallel and do not intersect

Front 3

Parallel Planes

Back 3

planes that do not intersect

Front 4

Parallel line and plane

Back 4

A line and a plane that do not intersect.

Front 5

Complete the theorem about parallel planes: If two parallel planes are cut by a third plane...

Back 5

then the lines of intersection are parallel

Front 6

Transversal

Back 6

A line that intersects two or more coplanar lines in different points

Front 7

Alternate Interior Angles

Back 7

two nonadjacent interior angles on opposite sides of the transversal

Front 8

Corresponding Angles(<->)

Back 8

two angles in corresponding positions relative to the two lines

Front 9

Same-side interior angles

Back 9

two interior angles on the same side of the transversal.

Front 10

Complete the postulate: If two parallel lines are cut by a transversal...

Back 10

then corresponding angles are congruent.

Front 11

Complete the theorem: If two parallel lines are cut by a transversal...

Back 11

then alternate interior angles are congruent.

Front 12

Complete the theorem about same-side interior angles: If two parallel lines are cut by a transversal...

Back 12

then same-side interior angles are supplementary

Front 13

Complete the theorem: If a transversal is perpendicular to one of two prallel lines...

Back 13

then it is perpendicular to the other one also

Front 14

Complete the postulate: If two lines are cut by a transversal and corresponding angles are congruent...

Back 14

then the lines are parallel

Front 15

Complete the theorem: If two lines are cut by a transversal and alternate interior angles are congruent...

Back 15

then the lines are parallel

Front 16

Complete the theorem: If two lines are cut by a transversal and same-side interior angles are supplementary...

Back 16

then the lines are parallel

Front 17

Complete the theorem: If two lines are in a plane and perpendicular to the same line...

Back 17

then the lines are parallel

Front 18

Complete the theorem: If a point is not on a line...

Back 18

then there is exactly one line through the point parallel to the given line

Front 19

Complete the theorem: If a point is not on a line...

Back 19

then there is exactly one line that passes through the point that is perpendicular to the given line

Front 20

Complete the theorem: If two lines are parallel to a third line...

Back 20

then they are parallel to each other

Front 21

How can you prove two lines are parallel?

Back 21

1. Show that a pair of corresponding angles are congruent.
2. Show that a pair of alternate interior angles are congruent.
3. Show that a pair of same-side interior angles are supplementary.
4. In a plane show that both lines are perpendicular to a third line.
5. Show that both lines are parallel to a third line.

Front 22

Triangle, Vertex, sides

Back 22

The figure formed by three segments joining three noncollinear points. Each of the points is called a vertex (plural vertices), the segments are called sides.

Front 23

Scalene triangle

Back 23

A triangle with no congruent sides.

Front 24

Equilateral triangle

Back 24

All sides are congruent

Front 25

Isosceles triangle

Back 25

a triangle with at least two congruent sides.

Front 26

Acute triangle

Back 26

Three acute angles

Front 27

Obtuse triangle

Back 27

one obtuse angle

Front 28

Right triangle

Back 28

one right angle

Front 29

Equiangular triangle

Back 29

all angles are congruent

Front 30

Auxillary line

Back 30

a line, ray or segment added to a diagram to help in a proof; it can only meet one condition

Front 31

Complete the theorem: The sum of the measures of....

Back 31

the angles of a triangle is 180

Front 32

Corollary

Back 32

A statement that can be proved by applying a theorem ( a sub-theorem)

Front 33

Complete the Corollary: If two angles of one triangle are congruent to two angles of...

Back 33

another triangle, then the third angles are congruent.

Front 34

Complete the Corollary: If two angles of one triangle are congruent to two angles of...

Back 34

another triangle, then the third angles are congruent.

Front 35

Complete the corollary: If a triangle is equiangular...

Back 35

then the measure of each angle is 60

Front 36

Complete the corollary: If a figure is a triangle...

Back 36

then there is at most one right angle or obtuse angle

Front 37

Complete the corollary: If a triangle is a right triangle...

Back 37

then the acute angles of the triangle are complementary

Front 38

Exterior angle

Back 38

the angle formed when one side of a triangle is extended

Front 39

Remote interior angles

Back 39

the two interior angles opposite an exterior angle of a triangle

Front 40

Complete the theorem: If a triangle has an exterior angle...

Back 40

then the measure of the exterior angle is equal to the sum of the measures of the remote interior angles

Front 41

Polygon

Back 41

A plane figure formed by coplanar segments (sides) such that
1. each segment intersacts exactly two other segments, one at each endpoint
2. no two segment with a common endpoint are collinear

Front 42

Convex Polygon

Back 42

a polygon such that no line containging a side of the polygon contains a point in the interior of the polygon.

Front 43

A polygon with three sides

Back 43

a triangle

Front 44

A polygon with four sides

Back 44

quadrilateral

Front 45

A polygon with five sides

Back 45

pentagon

Front 46

A polygon with six sides

Back 46

hexagon

Front 47

A polygon with seven sides

Back 47

heptagon

Front 48

A polygon with eight sides

Back 48

octagon

Front 49

A polygon with nine sides

Back 49

nonagon

Front 50

A polygon with ten sides

Back 50

decagon

Front 51

A polygon with 11 sides

Back 51

11-gon

Front 52

A polygon with 12 sides

Back 52

dodecagon

Front 53

A polygon with n sides

Back 53

n-gon

Front 54

Diagonal

Back 54

a segment joining two nonconsecutive vertices

Front 55

Complete the theorem: If a convex polygon has n sides...

Back 55

then the sum of the measures of the angles is (n-2)180

Front 56

Complete the theorem: If a convex polygon has one exterior angle at each vertex...

Back 56

then the sum of the measures of the exterior angles is 360

Front 57

Regular Polygon

Back 57

a polygon that is both equilateral and equiangular

Front 58

Inductive reasoning

Back 58

A type of reasoning in which the conclusion is based on several past observations