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.