Math 1
Terms
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- Linear pair
- 2 angles with one common side, that add up to 180 degrees
- skew lines*
- noncoplaner lines and cannot intersect
- Notation*
- _____ A is origin and B is the end point
- Things you may assume
- 1. Things that look straight are straight 2. Point of intersection are shown accurately 3. Points shown on a line are collinear. Unless planes are drawn, all points shown are coplaner 4. Relative positions of points are accurate.
- Angle-Addition Postulate*
-
If F is in the interior of < EHG, then m
- Theorem: angles, lines
- 1.Vertical angles are congruent 2. 2 perpendicular lines form 4 right angles
- Rotational symmetry
- the property that a figure can be rotated about some point onto itself through a rotation of between 0 and 360 degrees
- The length of a vector is the distence between A and B
- The direction of a vector is measured counter clockwise from the horizontal line.
- opposite rays*
- 2 collinear plane rays with the same end point that point in opposite directions.
- Center of Rotation
- the point about which a rotation turns
- parallel
- lines do not intersect
- Supplementary angles
- 2 angles whose measures add up to 180 degrees
- 3. Step to Bearings
- Because there are 360 degrees in a full circle, angles may be greater than 180 and will always have 3 digits. If you are measuring with a standard protractor, you will have to measure from the South point and add that measurement to 180.
- Translation
- is a transformation that moves all the points in a plane a fixed distance in a given direction.
- Definition of parallel/perpendicular
- 2 nonvertical lines are parallel if and only if their slopes are equal. 2 nonvertical lines are perpendicualr if and only if the product of their slopes is -1.
- Vertical angles*
- if 2 angles form 2 pairs of oppsite rays
- Angle bisector
- a ray that cuts an angle exactly in half
- sextant
- a navigational tool
- Translation Vector
- used to descride the direction and distence that each point travels.
- 1. Step to Bearings
- Locate north. The object you are measuring from will be on the center of your protractor and North will line up with your left 0 scale.
- parallel lines
- coplanar lines that do not intersect
- Isometric
- useing parallel edges on isometric graph paper to draw shape (usually cubes)
- Protractor Postulate*
-
If ray ___ is matched with the number r and ___ is matched with the number s, then m
- Rosette
- a design with rotational symmetry
- Rotation
- a transformation that turns a set of points about one point
- Linear-Pair Postulate
- the angles in a linear pair are supplementary
- Vector
- is a model of a straight lined path from one point to another
- Rotations preserve any property that has to do with the size of a figure including..
- 1. Length of sides 2. measure of angles 3. area 4. perimeter 5. rotations perserve the orientation
- Parallel Postulate*
- Through a given point, P, not on line__, exactly one line may be drawn parallel to line __.
- Theorem: Supp and comp angles
- 1. Supplements of congruent angles (or of the same angle) 2. Complements of congruent angles (or of the same angle) are congruent
- 2. Step to Bearings
- Measure the angle from 0 to the object your are measuring to.
- Half-turn
- a rotation of 180 degrees
- Theorem: angle
- all right angles are congruent
- Point symmetry
- the property that a figure will coincide with itself after some rotation of 180 degrees.
- Properties preserved by translations.
- 1. Lengths of the sides. 2. Measure of the angles. 3. Area and perimeter of the figure. 4. Orientation of the figure.
- Orthographic
- the view of an object when you look at the top, front, back, left, right. 2D/flat
- Things you may NOT assume (unless marked)
- 1. Exact measurements and relative sizes of figures 2. Parallel or perpendicular lines 3. Congruence
- Vector is NOT a Ray!
- A ray is a figure that begins at a point and travels in one direction forever, but a vector begins at a point going the same direction but does not go on forever.
- construction of an angle bisector**
- .
- Complementary angles
- 2 angles whose measures add up to 90 degrees
- Angle of rotation
- measures how much a point is turned about the center