Geometry Terms
Terms
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- midpoint
- C is the midpoint of segment A and B if C is between A and B and AC is congruent to CB
- equals of complements theorem
- if two angles are complementary to the same angle the the 2 angles are congruent
- point postulate
- a line contains atleast two points. a plane contains atleast 3 noncollinear points. space contains atleast 4 noncollinear points
- line postulate
- through any two points there exists exactly one line
- parallel at midpoints in a triangle theorem
- if a segment is drawn through 2 midpoints of two sides of a triangle: the segment is parallel to the third side. the segment is half the length of the third side
- isosceles trapezoid
- a trapezoid that has congruent legs
- same-side interior angles theorem
- it 2 parallel lines are cut by a transversal then same side interior angles are supplementary
- median of a trapezoid theorem
- the median of a trapezoid is parallel to both bases and the median is half the sum of the 2 bases
- vertical angles theorem
- vertical angles are congruent
- contrapositive
- if not p then not q
- parallels perpendicular theorem
- if a transversal is perpendicular to one of the two parallel lines then it is perpendicular to the other parallel.
- complementary angles
- two angles whose sum of measures is equal to 90 degrees
- square
- a parallelogram where all four angles are right angles and all four sides are congruent
- hypotenuse midpoint theorem
- if a median is drawn from the right angle of a right triangle to the midpoint, then the distance from that point to all three vertices are congruent
- ruler postulate
- every line can be made into a number line. distance between two points is the absolute value of the difference of their coordinates
- median of a trapezoid
- the segment joining the midpoints of the two legs
- trapezoid
- a quadrilateral with exactly one pair of parallel sides
- equals of supplements theorem
- if two angles are supplementary to the same angle then the two angles are congruent
- triangle inequality theorem
- the sum of any two sides of any triangle is always greater than the third side
- ratio
- A:B means A/B
- angle addition postulate
- if B is in the interior of angle XYZ then the measure of angle XYB plus the measure of angle BYZ = XYZ
- converse
- if q then p
- point, lines, plane theorem
- if two lines intersect then they lie on one plane together. a line and a point, not on the line, lie on a plane together
- supplementary angles
- two angles whose sum of measures is equal to 180 degrees
- segment addition postulate
- if B is between A and C then AB + AC = AC
- the sum of the angles of a polygon theorem
- the sum of the angles of a convex polygon that has N sides equals (N-2) x 180
- space
- a collection of all points
- protractor postulate
- we can draw a line dividing a plane into two 1/2 planes labelled AB. if C is between A and B then CB = 0 degrees, CA = 180 degrees and all rays drawn from C into the half plane has a measure between 0 degrees and 180 degrees
- conditional
- if p then q
- median of a triangle
- the segment drawn from a vertex to the midpoint of the opposite side
- rectangle
- a parallelogram that has four right angles. the diagonals are congruent
- adjacent angles
- two angles that share the same endpoint, share a common side, but no common interior point
- parallelogram
- a quadrilateral where both pairs of opposite sides are parallel
- altitude of a triangle
- the perpendicular drawn from the vertex to the opposite side
- angle
- a figure formed by two rays with a common endpoint
- postulate
- a statement we can accept to be true but can't prove to be true
- lines intersection theorem
- if two lines intersect, then the intersection is at exactly 1 point
- Euclidean postulate
- if two parallel lines are cut by a transversal, corresponding angles are congruent
- flat plane postulate
- if two points are on a plane, the the line drawn through the two points is entirely on the line
- theorem
- a statement we can prove to be true using other postulates, definitions, and theorems
- polygon
- a many sided closed figure
- inverse
- if not q then not p
- skew lines
- don't intersect but aren't collinear
- proportion
- an equation where 2 ratios are set equal to each other
- alternate interior angles are congruent
- if two parallel lines are cut by a transversal, then alternate interior angles are congruent
- quadrilateral
- a four sided polygon
- angle bisector
- a ray that divides an angle into two congruent adjacent angles
- isosceles trapezoid theorem
- the base angles of an isosceles trapezoid are congruent
- parallel lines
- two lines that are coplaner and don't intersect
- parallelogram bisector theorem
- the diagonals of a parallelogram bisect each other
- rhombus
- a parallelogram where all four sides are congruent. diagonals are perpendicular. a diagonal bisects both angles.
- segment AB
- the segment AB is the points A and B and all the points in between
- parallelogram theorem
- opposite sides of a parallelogram are congruent. opposite angles of a parallelogram are congruent
- perpendicular lines
- 2 lines that intersect and form four right triangles
- plane postulate
- through any 3 points there exists atleast one plane. through any 3 noncollinear points there exists exactly on one plane