Math lessons 1-4 Flashcards
Geometry:
A statement that defines a mathematical object
Undefined Term:
A basic mathematical term that is not defined using other mathematical terms.
Point:
Names a location and has no size
Line:
A straight path that has no thickness and goes for ever.
Collinear:
Points that lie on the same line.
Non- collinear:
Points that do not lie on the same line
Plane:
A flat surface that has no thickness and extends forever
Coplanar line:
Lines that lie on the same plain.
Non-coplanar Lines:
A line that does not contain points of other lines
Intersection:
The point or set of points in which two points meet.
Line segment:
Part of a line consisting of two endpoints and all points between them
Congruence Statement:
Shows that two segments are congruent
Tick Marks:
Placed on diagrams, objects, and shapes to show that lengths are congruent.
Postulate:
A segment that is accepted as true without having to explain it.
What are the three properties of Congruence?
Reflexive
Symmetric
Transitive
Reflexive:
Line AB is congruent to line BA: It’s like a mirror (Reflexive is one line)
Symmetric:
If line AB is congruent to Line CD then line CD is congruent to line AB ( Symmetric has two different lines)
Transitive:
If Line AB is congurrent to line CD and line CD is congruent to AB then line AB is congruent to EF. (transitive has 3 lines)
Distance:
The measure of the segment containing two points.
Midpoint:
The point that divides the segments into two congruent parts. Literally the middle point in a line.
Ray:
A part of a line that starts at an endpoint and extends infinitely in one direction. –.—–>
Angle:
A figure formed by two points with a common endpoint. .<
Vertex:
The common endpoint of an angle,
Protractor:
A tool used to measure angles
Degrees:
What angle measurements are measured in.
Acute:
Less than 90*
Obtuse:
More than 90* and less than 180*
Right:
90*
Straight:
180*
Bisect:
To divide into congruent parts.
Angle Bisector:
A ray that’s divides into an angle
Congruent Angles:
angles that have the same measurements
Steps to create congruent Angles
6 steps
Angles
1. create an angle
2. create a dot to the side and draw a line
3. Use compass to measure a comfortable length then make an arch.
4. Put arch on the other dot and line
5. Go to angle and measure the intersecting points and create an X, go do it to the other side.
6. wright angle ABC is congruent to angle FDE
Steps to creating congruent lines
- draw one line and create an arch on the top
- create a dot and measure with a compass how long the other line is then make the dots line that long.
- Wright line AB is congruent to line CD
If two lines intersect, then they intersect at one point.
This is because a curved line is not a line.
If there is a line and a point not on the line, then exactly one plant contains them
Theorem 4-2
If two lines intersect, there exists exactly one plane that contains them.
Theorme 4-3
Ruler Postulate:
The points on a line can be parried in the one-to-one correspondence with the real numbers such that: Any two given points can have the coordinates of 0 and 1
Segment Addition Postulate:
If B is between A and C, then AB and BC =AC
Protractor Postulate:
The rays formed on the protractor can be paired with real numbers form 0* to 180*
The Angle Addition Postulate:
M< ABD+M < DBC= M<ABC
Through two points there is exactly one line
there cannot be less than one line
Through any 3 noncollinear points there exists one plane
Only one plane cuz there are no lines
If two planes intersect then their is what?
A line connecting the two planes
A line contains at least 2 points:
A plane contains at least 3 non-collinear points. Space contains at least 4 non-collinear points.
