Geometry Ch 1 - Tools of Geometry Flashcards
Inductive Reasoning
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.
Conjecture
A conclusion you reach using inductive reasoning. Not all turn out to be true. You can prove the falsehood by finding one counterexample.
Counterexample
An example for which a conjecture is incorrect.
Isometric Drawing
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.
Orthographic Drawing
The top view, front view, and right-side view of a three-dimensional figure.
Foundation Drawing
Shows the base of a structure and the height of each part.
Example:
Net Drawing
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.
Geometric Point
A location. It has no size. It is represented by a small dot and is named by a capital letter.
Geometric Figure
A set of geometric points.
Geometric Shape
The set of all points.
Line
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.
Collinear Points
Points that lie on the same line.
Postulate / Axiom
An accepted statement of fact.
“Exactly One”
Means: There is one and there is no more than one.
How many lines exist through any two points?
Exactly one.
If two lines intersect, then they intersect at how many points?
Exactly one
When two planes intersect, how many lines do they form?
Exactly one.
How many planes exist through any three noncollinear points?
Exactly one
Segment
The part of a line consisting of two endpoints and all points between them.
Ray
The part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.
Opposite Rays
Two collinear rays with the same endpoint. They always form a line.
Are lines that do not intersect coplanar?
Maybe. Parallel lines are coplanar lines that do not intersect. Skew lines are noncoplanar; therefore they are not parallel and do not intersect.
Parallel Planes
Planes that do not intersect.
Ruler Postulate
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.
Congruent
Equal in size and similar in shape.
Symbol: ≅
Congruent Segments
Two segments with the same length.
Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC.
Midpoint
A point that divides a segment into two congruent segments.
Angle
Protractor Postulate
Angle Classifications
Congruent Angles
Angle Addition Postulate
Vertical Angles
Two angles whose sides are opposite rays.
Adjacent Angles
Two coplanar angles with a common side, a common vertex, and no common interior points.
Complementary Angles
Two angles whose measures have sum 90. Each angle is called the complement of the other.
Supplementary Angles
Two angles whose measures have sum 180. Each angle is called the supplement of the other.
Perpendicular Lines
Two lines that intersect to form right angles.
Symbol: ⊥
Perpendicular Bisector of a Segment
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.
Angle Bisector
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.
Coordinate Plane
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.
Distance Formula
Midpoint Formula
Distance in 3 Dimensions
Perimeter & Area of a Polygon
Finding Perimeter in the Coordinate Plane
If two figures are congruent, what does that imply about their areas?
The areas are the same.
How do you find the area of an irregular shape?
The area of a region is the sum of the areas of its nonoverlapping parts.
