Chapter 1 Overview

Question 1

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

Answer 1

Net, Isometric Drawing, Orthographic Drawing

Question 2

Net

Answer 2

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

Question 3

Isometric Drawing

Answer 3

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

Question 4

Orthographic Drawing

Answer 4

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

Question 5

point

Answer 5

indicates a location and has no side

Question 6

line

Answer 6

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

Question 7

plane

Answer 7

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

Question 8

collinear points

Answer 8

Pts that lie on the same line

Question 9

coplanar

Answer 9

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

Question 10

segment

Answer 10

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

Question 11

ray

Answer 11

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

Question 12

opposite rays

Answer 12

2 rays that share the same endpoint and form a line

Question 13

postulate

Answer 13

an accepted statement of fact

Question 14

Postulate 1-1

Answer 14

Through any 2 points there is exactly one line

Question 15

Postulate 1-2

Answer 15

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

Question 16

Postulate 1-3

Answer 16

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

Question 17

Postulate 1-4

Answer 17

Through any three noncollinear points there is exactly one plane

Question 18

Postulate 1-5: Ruler Postulate

Answer 18

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.

Question 19

Postulate 1-6: Segment Addition Postulate

Answer 19

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

Question 20

congruent segments

Answer 20

2 segments that have the same length

Question 21

midpoint

Answer 21

point that divides the segment into 2 congruent segments

Question 22

segment bisector

Answer 22

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

Question 23

angle

Answer 23

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

Question 24

interior of angle

Answer 24

region containing all of the pts between

The 2 sides of the angle

Question 25

exterior of angle

Answer 25

region containing all of the points outside of the angle

Question 26

Postulate 1-7: Protractor Postulate

Answer 26

For every angle corresponds a positive real number less than or equal to 180

Question 27

Postulate 1-8 Angle Addition Postulate

Answer 27

if we have two adjacent angles, we can add their measures to help us find unknown angles.

Question 28

adjacent angles

Answer 28

2 coplanar angles with a common side, common vertex and no common interior points

Question 29

vertical angles

Answer 29

2 nonadjacent angles formed by 2 intersecting lines; 2 angles whose sided are opposite rays

Question 30

complementary angles

Answer 30

2 angles whose measures have a sum of 90

Question 31

supplementary angles

Answer 31

2 angles whose measures have a sum of 180

Question 32

linear pair

Answer 32

pair of adjacent angles whose noncommon sides are opposite rays;
the angles of a linear pair form a straight line

Question 33

Postulate 1-9 Linear Pair Postulate

Answer 33

If 2 angles form a linear pair, then they are supplementary

Question 34

angle bisector

Answer 34

ray that divides an angle into two congruent angles

Question 35

construction

Answer 35

geometric figure drawn using a straightedge and compass

Question 36

Perpendicular lines

Answer 36

2 lines that intersect to form right angles ⊥ means “is perpendicular to”

Question 37

perpendicular bisector

Answer 37

line, segment, or ray that is perpendicular to the segment at its midpoint

Question 38

construction of congruent segment

Answer 38

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)

Question 39

Construction of Congruent Angles

Answer 39

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.

Question 40

Construction of a Perpendicular Bisector

Answer 40

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

Question 41

Constructing an Angle Bisector

Answer 41

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

Question 42

midpoint (in the coordinate plane)

Answer 42

the coordinates are the average of the x-coordinates and the average of the y-coordinates

Question 43

polygon

Answer 43

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

Question 44

convex polygon

Answer 44

no diagonal with points outside the polygon

Question 45

midpoint formula (in the coordinate plane)

Answer 45

x_1 + x_2 /2, y_1 + y_2 /2

Question 46

distance formula

Answer 46

d=√((x_2-x_1)²+(y_2-y_1)²)