Geometric Objects/Formulas
Quadrilaterals
They are four sided polygons and the sum of all their interior angles equal to 360 degrees. Types: Rectangle, Square, Parallelogram, Rhombus, and Trapezoid.
Rotation
Turning a figure around a fixed center point. When rotating at 90 degrees, or 270, the rule is to swap (x,y) coordinates to (y,x) and change signs on your y-values.
supplementary angles
Two angles whose sum is 180 degrees.
complementary angles
Two angles whose sum is 90 degrees.
Sphere
3-D version of a circle. It is every point that is the same distance from a single point. It contains a radius (distance from the center to the surface), diameter (straight line from one point to another that goes through center of sphere and it is twice the distance of the radius), and Pi (special number used with circles and spheres, it goes on forever but it abbreviated to 3.14).
Two-Dimensional shapes
A shape that has width and height and no thickness, also known as "2D".
Rhombus
All four sides have the same length.
Acute Triangle
All interior angles are less than 90 degrees. This is an oblique triangle because it does not have a 90 degree angle.
Equilateral Triangle
All three sides equal length and three angles of equal measure. All angles measure 60 degrees.
Obtuse angle
An angle that measures more than 90 degrees but less than 180 degrees.
Three-Dimensional Shapes
An object that has height, width, and depth known as "3D"
Possible Pythagorean Theorem problem on CSET
Assume that I-40 and I-50 run perpendicular to one another. Jim starts out in Amarillo and drives 1200 miles west on I-40, then 900 miles north 1-5. Approximately how far would he have traveled if he'd taken a direct flight from Amarillo to Portland? (1200)² + (900)² = c² 1,440,000 + 810,000 = 2,250,000. c² = 2,250,000 (find its square root) c = 1500 miles.
Parallelogram
Both opposing pairs of sides on a quadrilateral are parallel.
Triangles
Equilateral, Isosceles, Scalene, Right, Acute, and Obtuse.
Point Symmetry
Every part has a matching part.
Pentagon
Five sided polygon, and the sum of the interior angles is 540.
Reflection
Flipping a figure over a line of symmetry. When reflecting anything across the y-axis, all the y-values stay the same but the signs of the x-values change. Reflecting anything across the x-axis, the x-values remain the same but signs of y-values change.
Volume of a Rectangular Prism
Fomula: l x w x h Example: l = 12, w = 4, h = 3 12 x 4 x 3 = 144
Pythagorean Theorem
For any right triangle it states: a² + b² = c² leg + leg = Hypotenuse. Typically asks for the measure of the longest side, or distance between something. Example: Solve for c in the triangle below. a = 3, b = 4, c = ? 3² + 4² = c² 9 + 16 = 25 c² = 25 c = 5
Surface Area for Cylinder
Formula: 2πr^2 + 2πrh Translates to (2 x 3.14 x radius x radius) + (2 x 3.14 x radius x height). Example: What is the surface area of a cylinder with radius 3 cm and height 5 cm? (2 x 3.14 x 3 x 3) + (2 x 3.14 x 3 x 5) 56.52 + 94. 2 = 150.72 cm^2.
Surface Area of Sphere
Formula: 4πr^2 and answers should be in square units. Example: What is the surface area of a sphere that has a radius of 5 inches? 4 x 3.14 x 5 in x 5 in = 314 inches^2
Volume of a Cylinder
Formula: πr^2h or v = A (base) x h Translates to 3.14 x radius x radius x height. Example: Find the volume of a cylinder with radius 3 cm and height 5 cm? 3.14 x 3 x 3 x 5 = 141.3 cm³.
Trapezoid
Has only one pair of opposing parallel sides.
Cylinder
Has two circles on each end that are the same size and paralleled. It contains radius, height, and Pi.
Volume of Sphere
How much space takes up the inside of a sphere. Formula: 4/3πr^3 and answers should be in cubic units. Example: What is the volume of a sphere with a radius of 3 feet? 4/3 x 3.14 x 3 x 3 x 3 = 113.04 ft^3
Scalene Triangle
No sides that are the same length and no angles that are the same measure. All angles still add up to 180 degrees.
Reflection Symmetry
One half is the reflection of the other half.
Right Triangle
One of its angles is 90 degrees.
Obtuse Triangle
Opposite of Acute, it consists of one angle greater than 90 degrees. This is also oblique.
Hexagon
Six sided polygon with interior angles equal to 720 degrees.
Translation
Sliding a figure in any direction or distance. Moving all the points in the same direction, and same amount in that same direction.
Rotational Symmetry
The image is rotated around a central point so that it appears twice or more.
Line Symmetry
also known as Reflection, because it contains a line in the middle.
Right angle
an angle that measures 90 degrees.
Acute angle
an angle that measures less than 90 degrees.
Isosceles Triangle
has two sides that are the same length, and two angles that are the same measure.
Figures and Shapes Glossary/Terms
http://www.ducksters.com/kidsmath/figures_shapes_glossary.php
Alternate Exterior Angles Theorem
if two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
Alternate Interior Angels Theorem
if two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Corresponding Angles Postulate
if two parallel lines are cut by a transversal, then the corresponding angles are congruent.
Same Side Interior Angles Theorem
if two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
Rigid Transformations
in math, it is taking a set of points or coordinates and change them into a different set of coordinates or points - e.g. reflection, rotation, translation. Lengths and angles are preserved. However, if angles are preserved but lengths are scaled or stretched then they are not rigid transformations.
Parallel Lines
lines in the same plane that do not intersect.
Volume of Cylinder w/out radius given
radius = diameter/2 Ex: d = 14 in and h = 30 in r = 14/2 = 7 π(7)²(30) π(49)(30) π(1470) = 4,615 in³
Congruence
two or more objects are congruent if they have the same shape and size, though they may have been translated, rotated, or reflected.
Similarity
two or more objects are similar if they have the same shape, but different sizes.
Properties of Parallel Lines
when two parallel lines (a and m) are bisected by another line (t), all angles labeled (1,4,5,8) will have the same measure and all angles labeled (2,3,6,7) will have the same measure.
