Chapter 1 Overview Flashcards
What are the 3 techniques you can use to represent a 3D object with a 2D figure?
Net, Isometric Drawing, Orthographic Drawing
Net
a 2D diagram that you can fold to form a 3D figure; shows all of the surfaces of a figure in one view.
Isometric Drawing
shows a corner view of a 3D figure; allows you to see the top, front and side of the figure
Orthographic Drawing
shows 3 separate views: a top view, a front view, and a right-side view
point
indicates a location and has no side
line
represented by a straight path that extends in 2 opposite directions without end and has no thickness; contains infinitely many points
plane
represented by a flat surface that extends without end and has no thickness; contains infinitely many lines.
collinear points
Pts that lie on the same line
coplanar
points and lines that lie in the same plane; all the points of a line are coplanar
segment
part of a line that consists of 2 endpoints and all points between them
ray
part of a line that consists of one endpoint and all the points of the line one one side of the endpoint
opposite rays
2 rays that share the same endpoint and form a line
postulate
an accepted statement of fact
Postulate 1-1
Through any 2 points there is exactly one line
Postulate 1-2
If 2 distinct lines intersect, then they intersect in exactly one point
Postulate 1-3
If 2 distinct planes intersect, then they intersect in exactly one line
Postulate 1-4
Through any three noncollinear points there is exactly one plane
Postulate 1-5: Ruler Postulate
Every point on a line can be paired with a real number. This makes a one-to-one
correspondence between the points on the line and the real numbers. The real
number that corresponds to a point is called the coordinate of the point.
Postulate 1-6: Segment Addition Postulate
If 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC.
congruent segments
2 segments that have the same length
midpoint
point that divides the segment into 2 congruent segments
segment bisector
a point, line, line segment, ray, or plane that intersects the segment at its midpoint
angle
formed by 2 rays with the same endpoint
➢ The rays are the sides of the angle.
➢ The endpt is the vertex of the angle.
interior of angle
region containing all of the pts between
The 2 sides of the angle
exterior of angle
region containing all of the points outside of the angle
Postulate 1-7: Protractor Postulate
For every angle corresponds a positive real number less than or equal to 180
Postulate 1-8 Angle Addition Postulate
if we have two adjacent angles, we can add their measures to help us find unknown angles.
adjacent angles
2 coplanar angles with a common side, common vertex and no common interior points
vertical angles
2 nonadjacent angles formed by 2 intersecting lines; 2 angles whose sided are opposite rays
complementary angles
2 angles whose measures have a sum of 90
supplementary angles
2 angles whose measures have a sum of 180
linear pair
pair of adjacent angles whose noncommon sides are opposite rays;
the angles of a linear pair form a straight line
Postulate 1-9 Linear Pair Postulate
If 2 angles form a linear pair, then they are supplementary
angle bisector
ray that divides an angle into two congruent angles
construction
geometric figure drawn using a straightedge and compass
Perpendicular lines
2 lines that intersect to form right angles ⊥ means “is perpendicular to”
perpendicular bisector
line, segment, or ray that is perpendicular to the segment at its midpoint
construction of congruent segment
- Draw a segment XY
- Elsewhere on the paper, draw a line and a point on the line. Label the point P.
- Place the compass at point X and adjust the compass setting so that the pencil is at point Y.
- Using that setting, place the compass at point P and draw an arc that intersects the line. Label the point of intersection Q.
(https: //www.youtube.com/watch?v=oszaihGRIZ4)
Construction of Congruent Angles
- Using a straightedge, draw a reference line, if one is not provided.
- Place a dot (starting point) on the reference line.
- Place the point of the compass on the vertex of the given angle, ∠ABC (vertex at point B).
- Stretch the compass to any length that will stay “on” the angle.
- Swing an arc so the pencil will cross BOTH sides (rays) of the angle.
- Without changing the size of the compass, place the compass point on the starting point (dot) on the reference line and swing an arc that will intersect the reference line and go above the reference line.
- Go back to the given angle ∠ABC and measure the span (width) of the arc from where it crosses one side of the angle to where it crosses the other side of the angle. (Place a small arc to show you measured this distance.)
- Using this width, place the compass point on the reference line where the previous arc crosses the reference line and mark off this new width on your new arc.
- Connect this new intersection point to the starting point (dot) on your reference line.
- Label your copy.
Construction of a Perpendicular Bisector
- Draw a segment with endpoints A and B
- Put the point of the compass on A. Stretch out the compass until its more than half the length of AB.
- Draw an arc on either side of the line segment.
- Without changing the compass, put the point on B and draw an arc on either side of the segment
- Connect the X’s
Constructing an Angle Bisector
- Given an angle
- Create on arc of any size, such that it intersects both rays of the angle. Label those points B and C.
- Leaving the compass the same measurement, place your pointer on point B and create an arc in the interior of the angle
- Do the same step as 3 but placing your pointer at point C. Label the intersection D.
- Create ray AD. ray AD is the angle bisector
midpoint (in the coordinate plane)
the coordinates are the average of the x-coordinates and the average of the y-coordinates
polygon
closed plane figure formed by 3 or more segments ➢ each segment intersects exactly 2 other segments at their endpoints ➢ no 2 segments with a common endpt are collinear ➢ each segment called a side ➢ each endpt of a side is a vertex
convex polygon
no diagonal with points outside the polygon
midpoint formula (in the coordinate plane)
x_1 + x_2 /2, y_1 + y_2 /2
distance formula
d=√((x_2-x_1)²+(y_2-y_1)²)
