CCA Geometry - Hammond
Define Counterexample
An example used to prove that an if-then statement is false
Theorem 1-1: If 2 lines intersect then they intersect in _______ ______ _______
If two lines intersect then they interest in *exactly one point.*
Theorem 1-3: Complete the following: If two lines, intersect, then ______________________ plane contains the lines.
If two lines intersect, then *exactly one* plane contains the lines
Postulate 9 -- If two planes intersect, then their intersection is a ______.
If two planes intersect, then their intersection is a *line*
Postulate 8 -- If two points are in a plane, then the line that contains those points __________________________.
If two points are in a plane, then the line that contains those points is in that plane.
Define Angle
The space (usually measured in degrees) between two intersecting lines. Formed by two rays sharing a common endpoint called a vertex.
Define bisector.
Two bisect an object you cut it into two congruent parts. [Let's hope none of us get bisected;) ]
Define perpendicular lines.
Two lines are perpendicular if and only if they from right angles at their intersection.
Define Opposite rays
Two rays with a common endpoint that point in opposite directions and form a straight line.
Define Vertical Angles
Vertical angles are created when two lines cross and the angles are opposite of each other
What is the one undefined word, according to Euclid?
A point.
What is a line?
A length without width.
Postulate 5 - A line contains at least ____ points; a plane contains at least _____ points _____ all in one __________; space contains at least four points not ______ in one __________.
A line contains at least *2* points; a plane contains at least *3* points *not* all in one *line*; space contains at least four points not *all* in one *plane*.
What is a Postulate?
A statement that is accepted without a proof
What is a plane?
A two dimensional object that has infinite length and infinite width. There are no edges two planes.
What symbol represents the length of segment AB?
AB
Define straight angle
An angle measuring 180 degrees.
Define right angle
An angle measuring 90 degrees.
Define acute angle
An angle measuring less then 90 degrees.
Define obtuse angle
An angle measuring more then 90 degrees.
Midpoint theorem
If M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB
Define Complementary Angles
Complementary angles are two angles whose sum is 90 degrees
What are conditional statements?
Conditional statements are statements that can be written in an "if-then" form.
Define Congruent
Geometric figures that have the same size and shape.
State Theorem 2-5: 2 Congruent Adjacent Angles imply 2 Perpendicular Lines
If 2 lines form congruent adjacent angles, then the lines are perpendicular.
State the Straight Angle Postulate (Angle Addition Postulate Part 2) - If <AOC is a _______ angle and B is any point on line AC, then m<_____ + m<BOC = _____
If <AOC is a *straight* angle and B is any point on line AC, then *M<AOB* + m<BOC = *180*
Segment Add. Post.-- If B is between A and C, then _____ _____________________.
If B is between A and C, then *AB+BC=AC*
Given: If a, then b. What is the converse of the given statement?
If b, then a.
Angle Add. Post. Part 1-- If point B lies in the interior of <AOC, then m<____+m<_____=m<_____
If point B lies in the interior of <AOC, then m<*AOB*+m<*BOC*= m<*AOC*
State Theorem 2-6: Perpendicular Exterior Sides of Adjacent Angles imply Complementary Angles
If the exterior sides of 2 acute adjacent angles are perpendicular, then the angles are complimentary.
State Theorem 2-8, entitled Complements of Congruent Angles (or the Same Angle)
If two angles are complements of congruent (or of the same angle), then the two angles are *congruent*
State Theorem 2-7, entitled Supplements of Congruent Angles (or the Same Angle)
If two angles are supplements of congruent angles (or of the same angle ) then the two angles are congruent.
Define Supplementary Angles
Supplementary angles are two different angles whose sum is 180 degrees. If these two angles are adjacent they also form a straight angle.
How do you form the converse of a conditional statement?
Switch the hypothesis and conclusion.
Ruler Post. Part 2-- The distance between any ___ points equals the _________________________________.
The distance between any *2* points equals the *absolute value of the difference of their coordinates.*
Define vertex.
The vertex is the common endpoint that the two rays of angle share.
Theorem 1-2: Complete the following: Through a line and a point not in the line there is _________________ plane.
Through a line and a point not in the line there is *exactly one* plane
Postulate 6 - Through any ____ points there is ________ one line.
Through any *2* points there is *exactly* one line.
Postulate 7 - Through any three points there is ____ __________ one plane, and through any three ___-_________ points there is exactly one plane.
Through any three points there is *at least* one plane, and through any three *non-collinear* points there is exactly one plane.
Define Adjacent Angles
Two angles in a plane that have a common vertex and a common side but no common interior points
How do you form a biconditional statement from the two statements: If a, then b. and If b, then a.
a if and only if b.
What is a theorem?
a statement that can be proved
Angle Bisector Theorem: If ray BX is the ____ of <ABC, then m<ABX = __m<ABC and m<XBC = 1/2m<____.
bisector, 1/2, ABC.
Protractor Postulate (part b): If ray OP is paired with x, and ray OQ with y, then m<POQ = _____ (Or in other words to find the measure of an angle formed by two rays, what do you need to do?)
l x - y l
Theorem 2-4: If two lines are _______, then they form _______________ adjacent angles.
perpendicular, congruent
Define collinear.
points that are on the same line
Define biconditional statements
statements that contain the words "if and only if"
Define equidistant.
the same distant (equal distance)
Define space.
the set of all points
Define linear pair.
two adjacent angles whose measures add up to 180 degrees (Linear pair are also supplementary.)
What is the mid-point of a segment?
well... its a point in the middle of a segment that splits it into two congruent pieces... yeah, its pretty simple.
Define coplanar.
you guessed it. things are coplanar if the are all on the same plane.
