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Geometry mid-years term > geomtry term > Flashcards

geomtry term Flashcards

1
Q

Point

A

A specific location is space. Is is an undefined term…does not have an actual sizze.

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2
Q

Line

A

Determined by at least 2 points. Extends indefinitely on both sides.

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3
Q

Plane

A

a flat surface that extends indefinitely in all directions. Undefined term, no thickness.

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4
Q

Space

A

A boundless, three dimensional set of all points.

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5
Q

Line segment

A

A part of a line that consists of 2 points which the line has a definite length.

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6
Q

Collinear points

A

Points that lie on the same line.

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7
Q

Betweenness of Points

A

Point Y is between points X and Z if and only if X, Y, and Z are collinear and XY+YZ=XZ

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8
Q

Coplanar points

A

Points that lie on the same plane

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9
Q

Ray

A

An initial point and from that point a line extends indefinitely on one side only.

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10
Q

Intersect

A

Two or more geometric figures intersect if they have one or more points in common.

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11
Q

Congruent segments

A

Segments that have the same measure

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12
Q

Addition Postulate

A

If equal quantities are added to equal quantities, the sums are equal.

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13
Q

Subtraction Postulate

A

If equal quantities are subtracted from equal quantities, the differences are equal.

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14
Q

Multiplication Postulate

A

If equal quantities are multiplied by equal quantities, the products are equal. (also

Doubles of equal quantities are equal.)

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15
Q

Division Postulate

A

If equal quantities are divided by equal nonzero quantities, the quotients are equal.

(also Halves of equal quantities are equal.)

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16
Q

Substitution Postulate

A

A quantity may be substituted for its equal in any expression.

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17
Q

Partition Postulate

A

The whole is equal to the sum of its parts.

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18
Q

A Orthogonal
Pair

A

Two adjacent angles that are complementary.

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19
Q

Perpendicular lines

A

two lines that intersect to form right angles.

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20
Q

Perpendicular line Theorem

A

If 2 lines are perpendicular they form congruent adjacent angles.

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21
Q

Skew lines

A

non-coplanar lines. Therefore, they
are neither parallel nor intersecting.

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22
Q

Parallel lines

A

Lines that don’t intersect and have the same distance away from each other.

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23
Q

Parallel line theorem

A

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

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24
Q

Perpendicular line theorem

A

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

25
Q

How to prove lines are parallel?

A

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.

26
Q

Proving lines are Parallel postulate

A

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

27
Q

Scalene Triangle

A

A triangle with no congruent sides

28
Q

Isosceles Triangle

A

A triangle with at least 2 congruent sides.

29
Q

Equilateral Triangle

A

A triangle with 3 congruent sides.

30
Q

Equation for sum of Interior Angles

A

Number of sides-2 x 180

31
Q

Sum of exterior angles

A

360

32
Q

Exterior angle theorem

A

The sum of the
measures of the exterior angles of any convex
polygon, one angle at each vertex, is 360
degrees.

33
Q

The Isosceles Triangle Theorem

A

If two sides of a triangle are congruent, then angles opposite those sides are congruent

34
Q

Median

A

A median of a triangle is a segment from a vertex to the midpoint
of the opposite side.

35
Q

Altitude

A

An altitude of a triangle is the perpendicular segment from a
vertex to the line that contains the opposite side.

36
Q

Perpendicular Bisector

A

A perpendicular bisector of a segment is a line (or
ray or segment) that is perpendicular to the segment at its midpoint.

37
Q

Equal distant theorem 1

A

If a point lies on the perpendicular bisector of a segment, then the point is
equidistant from the endpoints of the segment.

38
Q

Equal distant theorem 2

A

If a point is equidistant from the endpoints of a segment, then the point lies
on the perpendicular bisector of the segment.

39
Q

Definition of a Parallelogram

A

Defined as a quadrilateral with 2 pairs of parallel sides

40
Q

Properties of a Parallelogram

A

Opposite sides are parallel, Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, The diagonals bisect each other, A diagonal divides the shape into 2 congruent triangles.

41
Q

How to prove a quadrilateral is a Parallelogram?

A

If both pairs of opposite sides of a quadrilateral are congruent, If both pairs of opposite angles of a quadrilateral are congruent, If one pair of opposite sides of a quadrilateral are both congruent and
parallel, If the diagonals of a quadrilateral bisect each other.

42
Q

Rectangle

A

A rectangle is a
parallelogram with one right angle.

43
Q

Properties of a Rectangle

A

All four right angles are right angles, The diagonals are congruent.

44
Q

How to prove a quadrilateral is a rectangle?

A

It is a parallelogram and one of the
angles is a right angle. It is a parallelogram whose diagonals are congruent. All four angles are right angles. It is equiangular.

45
Q

Rhombus

A

A rhombus is a quadrilateral with 4 congruent sides.

46
Q

Properties of a Rhombus

A

All four sides are congruent. The diagonals are perpendicular to each other. The diagonals bisect their angles.

47
Q

How to prove a quadrilateral is a Rhombus?

A

It is a parallelogram with two congruent consecutive sides. It is a parallelogram and the diagonals are perpendicular to each other. It is a parallelogram and each diagonal bisects the angles whose vertices it joins. All four sides are congruent.

48
Q

Square

A

A square is a rectangle
that has two congruent consecutive
sides.

49
Q

How to prove a quadrilateral is a Square?

A

It is a rectangle with two consecutive sides congruent. It is a rhombus and one of the angles is a right angle. It has four right angles and four congruent sides.

50
Q

Properties of a square

A

A square has all the properties of a rectangle. A square has all the properties of a rhombus.

51
Q

Trapezoid

A

A trapezoid is a quadrilateral with at least one pair of parallel sides.

52
Q

Isosceles Trapezoids

A

An isosceles trapezoid is a
trapezoid with one pair of congruent
base angles.

53
Q

Properties of an Isosceles Trapezoid

A

Both pairs of base angles of an
isosceles trapezoid are congruent. The legs of an isosceles trapezoid
are congruent. The diagonals of an isosceles
trapezoid are congruent.

54
Q

Midsegment of a Triangle -1

A

A line that contains the
midpoint of one side of a triangle and is
parallel to another side passes through
the midpoint of the third side.

55
Q

Midsegment of a Triangle - 2

A

The segment that joins the
midpoints of two sides of a triangle
(mid-segment). 1)is parallel to the third side; 2)is half as long as the third side.

56
Q

Midsegment of a Trapezoid

A

Parallel to the base

½ length of the base

The midsegment of a trapezoid
joins the midpoints of its legs.

The midsegment of a Trapezoid is the average length of the parallel lines.

57
Q

Area of a parallelogram

A

Base x Height

58
Q

Area of a Rhombus(Kite)

A

(Diagonal 1 x Diagonal 2)/2

59
Q

Area of a Trapezoid

A

((Base 1 + Base 2)/2) x Height

Geometry mid-years term (2 decks)

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