Chapter 1 Overview Flashcards

1
Q

What are the 3 techniques you can use to represent a 3D object with a 2D figure?

A

Net, Isometric Drawing, Orthographic Drawing

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2
Q

Net

A

a 2D diagram that you can fold to form a 3D figure; shows all of the surfaces of a figure in one view.

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3
Q

Isometric Drawing

A

shows a corner view of a 3D figure; allows you to see the top, front and side of the figure

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4
Q

Orthographic Drawing

A

shows 3 separate views: a top view, a front view, and a right-side view

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5
Q

point

A

indicates a location and has no side

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6
Q

line

A

represented by a straight path that extends in 2 opposite directions without end and has no thickness; contains infinitely many points

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7
Q

plane

A

represented by a flat surface that extends without end and has no thickness; contains infinitely many lines.

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8
Q

collinear points

A

Pts that lie on the same line

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9
Q

coplanar

A

points and lines that lie in the same plane; all the points of a line are coplanar

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10
Q

segment

A

part of a line that consists of 2 endpoints and all points between them

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11
Q

ray

A

part of a line that consists of one endpoint and all the points of the line one one side of the endpoint

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12
Q

opposite rays

A

2 rays that share the same endpoint and form a line

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13
Q

postulate

A

an accepted statement of fact

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14
Q

Postulate 1-1

A

Through any 2 points there is exactly one line

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15
Q

Postulate 1-2

A

If 2 distinct lines intersect, then they intersect in exactly one point

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16
Q

Postulate 1-3

A

If 2 distinct planes intersect, then they intersect in exactly one line

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17
Q

Postulate 1-4

A

Through any three noncollinear points there is exactly one plane

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18
Q

Postulate 1-5: Ruler Postulate

A

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.

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19
Q

Postulate 1-6: Segment Addition Postulate

A

If 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC.

20
Q

congruent segments

A

2 segments that have the same length

21
Q

midpoint

A

point that divides the segment into 2 congruent segments

22
Q

segment bisector

A

a point, line, line segment, ray, or plane that intersects the segment at its midpoint

23
Q

angle

A

formed by 2 rays with the same endpoint
➢ The rays are the sides of the angle.
➢ The endpt is the vertex of the angle.

24
Q

interior of angle

A

region containing all of the pts between

The 2 sides of the angle

25
exterior of angle
region containing all of the points outside of the angle
26
Postulate 1-7: Protractor Postulate
For every angle corresponds a positive real number less than or equal to 180
27
Postulate 1-8 Angle Addition Postulate
if we have two adjacent angles, we can add their measures to help us find unknown angles.
28
adjacent angles
2 coplanar angles with a common side, common vertex and no common interior points
29
vertical angles
2 nonadjacent angles formed by 2 intersecting lines; 2 angles whose sided are opposite rays
30
complementary angles
2 angles whose measures have a sum of 90
31
supplementary angles
2 angles whose measures have a sum of 180
32
linear pair
pair of adjacent angles whose noncommon sides are opposite rays; the angles of a linear pair form a straight line
33
Postulate 1-9 Linear Pair Postulate
If 2 angles form a linear pair, then they are supplementary
34
angle bisector
ray that divides an angle into two congruent angles
35
construction
geometric figure drawn using a straightedge and compass
36
Perpendicular lines
2 lines that intersect to form right angles ⊥ means “is perpendicular to”
37
perpendicular bisector
line, segment, or ray that is perpendicular to the segment at its midpoint
38
construction of congruent segment
1. Draw a segment XY 2. Elsewhere on the paper, draw a line and a point on the line. Label the point P. 3. Place the compass at point X and adjust the compass setting so that the pencil is at point Y. 4. 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)
39
Construction of Congruent Angles
1. Using a straightedge, draw a reference line, if one is not provided. 2. Place a dot (starting point) on the reference line. 3. Place the point of the compass on the vertex of the given angle, ∠ABC (vertex at point B). 4. Stretch the compass to any length that will stay "on" the angle. 5. Swing an arc so the pencil will cross BOTH sides (rays) of the angle. 6. 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. 7. 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.) 8. 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. 9. Connect this new intersection point to the starting point (dot) on your reference line. 10. Label your copy.
40
Construction of a Perpendicular Bisector
1. Draw a segment with endpoints A and B 2. Put the point of the compass on A. Stretch out the compass until its more than half the length of AB. 3. Draw an arc on either side of the line segment. 4. Without changing the compass, put the point on B and draw an arc on either side of the segment 5. Connect the X's
41
Constructing an Angle Bisector
1. Given an angle 2. Create on arc of any size, such that it intersects both rays of the angle. Label those points B and C. 3. Leaving the compass the same measurement, place your pointer on point B and create an arc in the interior of the angle 4. Do the same step as 3 but placing your pointer at point C. Label the intersection D. 5. Create ray AD. ray AD is the angle bisector
42
midpoint (in the coordinate plane)
the coordinates are the average of the x-coordinates and the average of the y-coordinates
43
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 ```
44
convex polygon
no diagonal with points outside the polygon
45
midpoint formula (in the coordinate plane)
x_1 + x_2 /2, y_1 + y_2 /2
46
distance formula
d=√((x_2-x_1)²+(y_2-y_1)²)