geomtry term Flashcards
Point
A specific location is space. Is is an undefined term…does not have an actual sizze.
Line
Determined by at least 2 points. Extends indefinitely on both sides.
Plane
a flat surface that extends indefinitely in all directions. Undefined term, no thickness.
Space
A boundless, three dimensional set of all points.
Line segment
A part of a line that consists of 2 points which the line has a definite length.
Collinear points
Points that lie on the same line.
Betweenness of Points
Point Y is between points X and Z if and only if X, Y, and Z are collinear and XY+YZ=XZ
Coplanar points
Points that lie on the same plane
Ray
An initial point and from that point a line extends indefinitely on one side only.
Intersect
Two or more geometric figures intersect if they have one or more points in common.
Congruent segments
Segments that have the same measure
Addition Postulate
If equal quantities are added to equal quantities, the sums are equal.
Subtraction Postulate
If equal quantities are subtracted from equal quantities, the differences are equal.
Multiplication Postulate
If equal quantities are multiplied by equal quantities, the products are equal. (also
Doubles of equal quantities are equal.)
Division Postulate
If equal quantities are divided by equal nonzero quantities, the quotients are equal.
(also Halves of equal quantities are equal.)
Substitution Postulate
A quantity may be substituted for its equal in any expression.
Partition Postulate
The whole is equal to the sum of its parts.
A Orthogonal
Pair
Two adjacent angles that are complementary.
Perpendicular lines
two lines that intersect to form right angles.
Perpendicular line Theorem
If 2 lines are perpendicular they form congruent adjacent angles.
Skew lines
non-coplanar lines. Therefore, they
are neither parallel nor intersecting.
Parallel lines
Lines that don’t intersect and have the same distance away from each other.
Parallel line theorem
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
Perpendicular line theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular
to the other one also.
How to prove lines are parallel?
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.
Proving lines are Parallel postulate
If two lines are cut by a transversal and corresponding angles are
congruent, then the lines are parallel.
Scalene Triangle
A triangle with no congruent sides
Isosceles Triangle
A triangle with at least 2 congruent sides.
Equilateral Triangle
A triangle with 3 congruent sides.
Equation for sum of Interior Angles
Number of sides-2 x 180
Sum of exterior angles
360
Exterior angle theorem
The sum of the
measures of the exterior angles of any convex
polygon, one angle at each vertex, is 360
degrees.
The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then angles opposite those sides are congruent
Median
A median of a triangle is a segment from a vertex to the midpoint
of the opposite side.
Altitude
An altitude of a triangle is the perpendicular segment from a
vertex to the line that contains the opposite side.
Perpendicular Bisector
A perpendicular bisector of a segment is a line (or
ray or segment) that is perpendicular to the segment at its midpoint.
Equal distant theorem 1
If a point lies on the perpendicular bisector of a segment, then the point is
equidistant from the endpoints of the segment.
Equal distant theorem 2
If a point is equidistant from the endpoints of a segment, then the point lies
on the perpendicular bisector of the segment.
Definition of a Parallelogram
Defined as a quadrilateral with 2 pairs of parallel sides
Properties of a Parallelogram
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.
How to prove a quadrilateral is a Parallelogram?
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.
Rectangle
A rectangle is a
parallelogram with one right angle.
Properties of a Rectangle
All four right angles are right angles, The diagonals are congruent.
How to prove a quadrilateral is a rectangle?
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.
Rhombus
A rhombus is a quadrilateral with 4 congruent sides.
Properties of a Rhombus
All four sides are congruent. The diagonals are perpendicular to each other. The diagonals bisect their angles.
How to prove a quadrilateral is a Rhombus?
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.
Square
A square is a rectangle
that has two congruent consecutive
sides.
How to prove a quadrilateral is a Square?
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.
Properties of a square
A square has all the properties of a rectangle. A square has all the properties of a rhombus.
Trapezoid
A trapezoid is a quadrilateral with at least one pair of parallel sides.
Isosceles Trapezoids
An isosceles trapezoid is a
trapezoid with one pair of congruent
base angles.
Properties of an Isosceles Trapezoid
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.
Midsegment of a Triangle -1
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.
Midsegment of a Triangle - 2
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.
Midsegment of a Trapezoid
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.
Area of a parallelogram
Base x Height
Area of a Rhombus(Kite)
(Diagonal 1 x Diagonal 2)/2
Area of a Trapezoid
((Base 1 + Base 2)/2) x Height
