Theorems
Terms
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- hypothesis
- the "if" clause
- Euler diagram
- circle diagrams that show how conditional statements relate to each other
- angle
- a pair of rays that have the same endpoint
- straightedge
- used for drawing lines
- coplanar
- 3 or more points on a plane
- point
- "that which has no part"; a specific location
- line
- described as having "breadthless length"
- line segment
- part of a line bounded by two endpoints; has length and can be measured
- postulate 1
- two points determine a line
- perimeter
- sum of the length of the sides
- ray
- part of a line that extends endlessly in one direction
- collinear
- 3 or more points on the same line
- plane
- a flat surface
- concurrent
- multiple lines that contain the same point
- postulate
- a statement that is assumed to be true without proof
- noncollinear
- 3 or more points that one line can't contain
- postulate 2
- three noncollinear points determine a plane
- Two Circle Theorems
- if the diameter of a circle is d, its circumference is pi d; if the radius of a circle is r, its area is pi r sq.
- Pythagorean Theorem
- the sq. of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides
- perimeter formula
- A=lw
- polyhedron
- bounded by polygons and exists in space; three dimensional object
- converse
- interchanging the hypothesis and conclusion
- Triangle Angle Sum THeorem
- the sum of the angles of a triangle is 180 degrees
- theorem
- a statement that is proved by reasoning deductively from already accepted statements
- conditional statement
- consists of 2 clauses, one of which begins with the word "if" and the other "then"
- conclusion
- the "then" clause
- direct proof
- just like def. of syllogism
- compass
- used for drawing circles
- syllogism
- if a, then b; if b, then c; if a, then c
- polygon
- bounded by line segments; lies in a plane
- IFF
- if and only if
- circle
- the set of all points in a plane that are a fixed distance from a given point in a plane
- indirect proof
- using the "contradiction"