Geometry Ch 1 - Tools of Geometry

Question 1

Inductive Reasoning

Answer 1

reasoning that is based on patterns you observe. If you observe a pattern in a sequence, you can use inductive reasoning to tell what the next terms in the sequence will be.

Question 2

Conjecture

Answer 2

A conclusion you reach using inductive reasoning. Not all turn out to be true. You can prove the falsehood by finding one counterexample.

Question 3

Counterexample

Answer 3

An example for which a conjecture is incorrect.

Question 4

Isometric Drawing

Answer 4

A drawing of a three dimensional object showing a comer view of a figure. It is not drawn in perspective and distances are not distorted.

Question 5

Orthographic Drawing

Answer 5

The top view, front view, and right-side view of a three-dimensional figure.

Question 6

Foundation Drawing

Answer 6

Shows the base of a structure and the height of each part.

Example:

Question 7

Net Drawing

Answer 7

A two-dimensional pattern that you can fold to form a three·dimensional figure. It shows all of the surfaces of a figure in one view.

Question 8

Geometric Point

Answer 8

A location. It has no size. It is represented by a small dot and is named by a capital letter.

Question 9

Geometric Figure

Answer 9

A set of geometric points.

Question 10

Geometric Shape

Answer 10

The set of all points.

Question 11

Line

Answer 11

A series of points that extends in two opposite directions without end. It is usually “named” by using two points, or with a single lowercase letter.

Question 12

Collinear Points

Answer 12

Points that lie on the same line.

Question 13

Postulate / Axiom

Answer 13

An accepted statement of fact.

Question 14

“Exactly One”

Answer 14

Means: There is one and there is no more than one.

Question 15

How many lines exist through any two points?

Answer 15

Exactly one.

Question 16

If two lines intersect, then they intersect at how many points?

Answer 16

Exactly one

Question 17

When two planes intersect, how many lines do they form?

Answer 17

Exactly one.

Question 18

How many planes exist through any three noncollinear points?

Answer 18

Exactly one

Question 19

Segment

Answer 19

The part of a line consisting of two endpoints and all points between them.

Question 20

Ray

Answer 20

The part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.

Question 21

Opposite Rays

Answer 21

Two collinear rays with the same endpoint. They always form a line.

Question 22

Are lines that do not intersect coplanar?

Answer 22

Maybe. Parallel lines are coplanar lines that do not intersect. Skew lines are noncoplanar; therefore they are not parallel and do not intersect.

Question 23

Parallel Planes

Answer 23

Planes that do not intersect.

Question 24

Ruler Postulate

Answer 24

The points of a line can be put in to one -to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers.

Question 25

Congruent

Answer 25

Equal in size and similar in shape. Symbol: ≅

Question 26

Congruent Segments

Answer 26

Two segments with the same length.

Question 27

Segment Addition Postulate

Answer 27

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

Question 28

Midpoint

Answer 28

A point that divides a segment into two congruent segments.

Question 29

Angle

Answer 29

Question 30

Protractor Postulate

Answer 30

Question 31

Angle Classifications

Answer 31

Question 32

Congruent Angles

Answer 32

Question 33

Angle Addition Postulate

Answer 33

Question 34

Vertical Angles

Answer 34

Two angles whose sides are opposite rays.

Question 35

Adjacent Angles

Answer 35

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

Question 36

Complementary Angles

Answer 36

Two angles whose measures have sum 90. Each angle is called the *complement* of the other.

Question 37

Supplementary Angles

Answer 37

Two angles whose measures have sum 180. Each angle is called the *supplement* of the other.

Question 38

Perpendicular Lines

Answer 38

Two lines that intersect to form right angles. Symbol: **⊥**

Question 39

Perpendicular Bisector of a Segment

Answer 39

A line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment into two congruent segments. There is just one line that is the perpendicular bisector of a segment in a given plan.

Question 40

Angle Bisector

Answer 40

A ray that divides an angle into two congruent coplanar angles. Its endpoint is at the angle vertex. Within the ray, a segment with the same endpoint is also an angle bisector. You may say that the ray or segment *bisects* the angle.

Question 41

Coordinate Plane

Answer 41

An important tool for working with equations. It is formed by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. The two axes intersect at a point called the origin.

Question 42

Distance Formula

Answer 42

Question 43

Midpoint Formula

Answer 43

Question 44

Distance in 3 Dimensions

Answer 44

Question 45

Perimeter & Area of a Polygon

Answer 45

Question 46

Finding Perimeter in the Coordinate Plane

Answer 46

Question 47

If two figures are congruent, what does that imply about their areas?

Answer 47

The areas are the same.

Question 48

How do you find the area of an irregular shape?

Answer 48

The area of a region is the sum of the areas of its nonoverlapping parts.