Week 12 Flashcards
Direct comparisons
Placing two objects next to each other to determine which is longer or taller
Indirect comparisons
Using a third object to make an indirect comparison between two objects
Transitive property
A relation ~ between quantities such that if X ~ Y and Y ~ Z, then X ~ Z
Perimeter
Distance around a polygon or closed curve
Circumference
Length of a circle
Process of measurement
A process that involves matching an attribute of an object with an (often repeated) unit, which is a different object having the same attribute
Unit
In measurements, the size of the comparison object, ie. mile
Metric system or SI
Most common international system of standard units for measurement, meters, centimeters, etc.
Meter
The basic metric system unit of measurement of length or distance; about 39.37 inches or 1.09 yards
List the common metric prefixes in order, smallest to largest
millimeter, centimeter, decimeter, meter, decameter, hectometer, kilometer
Measurements are exact T/F
False
Counts are exact T/F
True
List 3 ways of conceptualizing angles
Structure, space, rotation
Degree
For angle measurement, the size of an angle formed by a ray 1/360 of a full turn from the other ray of the angle. Hence, 360 degrees in a full turn
A minute (‘) for angle size is
1/60 of a degree
A second (“) for angle size is
1/60 of a minute
Vertical angles (opposite angles)
The nonadjacent angles formed when two lines cross
Corresponding angles
In congruent or similar shapes, angles that match, or angles that match when two lines are crossed by a third line
Alternate interior angles
Angles in the corners of a Z shape
Area
The amount of two-dimensional space occupied by a shape or surface. How much “surface” a shape has
Standard units
Square regions with sides whose lengths are all 1 length unit
Metric system’s basic unit for measuring area
Square meter
Are
“air” symbol a, 100m^2
Hectare
(ha) a metric square unit equal to 100 ares
Surface area
Sum of the areas of a 3D shape
Congruent shapes have the same areas T/F
True
Shapes with the same area are congruent T/F
False
Volume
The quantity of space occupied
Standard unit for volume
Cubic inch
Liter
Metric system, smaller than cubic meter, about 1.06 quarts
1 liter in cubic decimeters
1
Formula for similar 3D shapes volume
new volume = k^3 x original volume
Circumference formula
C = (pi)d
Formula for area of rectangular region
lw or bh
A (square region) =
s^2 or s squared
A(parallelogram region) =
bh
A(triangular region) =
1/2 bh
A height of a triangle is called
Altitude
A(trapezoidal region) =
1/2 h(a+b) where a is top and b is bottom
Every polygonal region can be cut into triangular regions T/F
True
A(circular region) =
(pi)r^2
Radius is half of the diameter T/F
True
Diameter is half of the radius T/F
False
A(surface of a sphere) =
4(pi)r^2 where r is the radius of the sphere
Surface area of a polyhedron =
sum of area of its faces
V(prism or cylinder) =
Bh where B is the area of the base and h is the height of the prism or cylinder
Does V=Bh also apply to oblique prisms?
Yes
V(pyramids and cones) =
1/3Bh
V(sphere) =
4/3(pi)r^3
Legs of right triangle
Either of the two sides making the right angle
Hypotenuse
Side of a triangle opposite the right angle
Pythagorean theorem
a^2 + b^2 = c^2
Distance formula
d = square root of (x1-x2)^2 + (y1-y2)^2
