Vocabulary
Postulates
Constructions
Midpoint & Distance
Inductive Reasoning
100
Points are ____________ if they lie on the same line.
Collinear
100
True or False? ∠ ADB + ∠ BDC = ∠ ADC.
True. Part + part = whole
100
A __________ __________ of a segment is a line, segment, or ray that is perpendicular to the segment and divides the segment into two congruent segments.
Perpendicular Bisector
100
Find Midpoint: A(-3,-5) B(7,9)
M(2, 2)
100
A ______________ is an unproven statement or rule that is based on inductive reasoning.
Conjecture
200
A ________ is an infinite number of points on a straight path that extends in two opposite directions.
Line
200
If points A, B, and C are collinear and B is between A and C, then ______ + ______ = _______ (Segment Addition Postulate)
AB + BC = AC
200
An ________ _________ is a ray that divides an angle into two congruent angles.
Angle bisector
200
Find the distance between A(0,0) and B(4,5)
√41
200
How many penguins are in the next figure?
11
300
A __________ is an exact location and has no size.
Point
300
Point B is between A and C. If AB = 15 and BC = 7, find AC.
22
300
49 degrees
300
Find Midpoint: A(1,-3) B(3,5)
M(2, 1)
300
What is the next number in the number pattern?
0, 2, 5, 7, 10, 12, 15, ______
Pattern is +2, +3 so the next number would be
15 + 2 = 17
400
An _______ is the space (measured in degrees) between two rays.
Angle
400
If ∠ ABC = 47 degrees, what is the value of x?
x = 7
400
Before you begin constructing a perpendicular bisector, how wide does your compass need to be?
Greater than half of the segment you are bisecting.
400
Find the distance between (2,9) and (1,5)
√17
400
Is the conjecture below true or false?
The difference of two integers is an integer.
True.
1 - 4 = -3
8 - 2 = 6
-2 - -4 = 2
500
A ______________ is a case in which the conjecture is proven false.
Counterexample
500
If AC = 13, what is the value of x?
x = 3
500
What tool do you need to use in the last step of creating an angle bisector?
A straightedge to draw the ray bisecting the angle.
500
What are two differences between the midpoint and distance formulas?
m = [ (x2+x1)/2 , (y2+y1)/2 ]
d = √ (x2 - x1)^2 + (y2 - y1)^2
1) midpoint you add the x and y values, distance you subtract the x and y values
2) distance you take the square root, midpoint there is no squaring or taking the square root
500
Prove the conjecture below is false with a counterexample.
1, 9, 25, 49... are all perfect squares and odd.