Unit 1 Visual Glossary By Patrick
Lesson 1 Terms
Point- names a location and has no size. It is represented by a dot.
The point on the left has no thickness.
The point on the left has no thickness.
Line- a straight path that has no thickness and extends forever. Notated with a double arrow.
Line AB is defined by letters A and B.
Line AB is defined by letters A and B.
Plane- a flat surface that has no thickness and extends forever.
Plane ABC is determined by 3 points, because any three non-collinear points can define a plane.
Plane ABC is determined by 3 points, because any three non-collinear points can define a plane.
Collinear Points- points that lie on the same line.
The points shown are collinear.
The points shown are collinear.
Coplanar Points- points that lie in the same plane.
The points all reside on the same plane.
The points all reside on the same plane.
Line Segment- the part of a line consisting of two points and all points between them. Notated with a line above the letters.
Segment AB is a part of line AB.
Segment AB is a part of line AB.
Endpoint- a point at the end of a segment or the starting point of a ray.
Point A is an endpoint of segment AB.
Point A is an endpoint of segment AB.
Ray- a part of a line that starts at an endpoint and extends forever in one direction.
Ray AB extends forever.
Notated with an arrow above the letters.
Ray AB extends forever.
Notated with an arrow above the letters.
Opposite Rays- two rays that have a common endpoint and form a line.
AC and AB are opposite rays.
AC and AB are opposite rays.
Postulate- Also called an axiom, it is a statement that is accepted as true without proof.
The image to the left is a postulate.
The image to the left is a postulate.
Intersection- the set of all points that two or more figures have in common.
Lines AC and DE intersect at point B.
Lines AC and DE intersect at point B.
Lesson 2 Terms
Inductive Reasoning- the process of reasoning that a rule or statement is true because specific cases are true.
The image on the left shows steps in Inductive Reasoning.
The image on the left shows steps in Inductive Reasoning.
Conjecture- a statement believed to be true based on inductive reasoning.
A conjecture is stated on the left, and it reads 'segment AM congruent to segment MB'.
A conjecture is stated on the left, and it reads 'segment AM congruent to segment MB'.
Counterexample- a specific example that shows a statement of conjecture is false.
On the left, a counterexample is printed in red.
On the left, a counterexample is printed in red.
Deductive Reasoning- the process of using logic to draw conclusions based on given facts, definitions, and properties.
The left image follows the process of deductive reasoning.
The left image follows the process of deductive reasoning.
Lesson 3 Terms
Conditional Statement- a statement that can be written in the form "if p, then q."
The statement on the left is written as "if p, then q".
The statement on the left is written as "if p, then q".
Hypothesis- the part p of a conditional statement following the word if.
The text in blue is a hypothesis.
The text in blue is a hypothesis.
Conclusion- the part q of a conditional statement following the word then.
The text in green above is part of the conclusion.
The text in green above is part of the conclusion.
Truth Value- A conditional statement has a truth value of either true (T) or false (F).
The statement in the image have opposite truth values.
The statement in the image have opposite truth values.
Negation- Negation of a statement p is "not p," written as ~p. P and Q are negated on the left.
Converse- the statement formed by exchanging the hypothesis and conclusion.
The statement above is converse.
The statement above is converse.
Inverse- the statement formed by negating the hypothesis and conclusion. The statement on the left is an inverse.
Contrapositive- the statement formed by both exchanging and negating the hypothesis and conclusion. The statement on the left is contrapositive.
Logically Equivalent Statements- related conditional statements that have the same truth value. are called logically equivalent statements.
Inverses and converses of the same statement are logically equivalent.
Inverses and converses of the same statement are logically equivalent.
Biconditional Statement- a statement that can be written in the form "p if and only if q." This means "if p then q" and
"if q then p."
"if q then p."
Definition- a statement that describes an object and can be written as a true biconditional.
Polygon- a closed plane figure formed by three or more segments, where each segment intersects exactly two other
segments only at their endpoints and no two segments with a common endpoint are collinear.
The image on the left is closed, and it has all sides made of segments, so it is a polygon.
segments only at their endpoints and no two segments with a common endpoint are collinear.
The image on the left is closed, and it has all sides made of segments, so it is a polygon.
Triangle- is a three-sided polygon.
Since the image is a polygon, and three sided, it is a triangle.
Since the image is a polygon, and three sided, it is a triangle.
Quadrilateral- a four-sided polygon.
The image of a polygon to the right is a quadrilateral, because it has four sides.
The image of a polygon to the right is a quadrilateral, because it has four sides.
Lesson 4 Terms
Proof- an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion
is true. The proof above is done for-8 = 5n + 2.
is true. The proof above is done for-8 = 5n + 2.
Lesson 6 Terms
Coordinate- a number used to identify the location of a point. On a number line, a point corresponds to one number and this number is called a coordinate.
The diagram on the left shows the coordinates (3,4).
The diagram on the left shows the coordinates (3,4).
Distance- distance between any two points is the absolute value of the difference of the coordinates. The distance between two points A and B is also called the length of AB.
On the right triangle diagram, distance across the red segment is represented by 'd'.
On the right triangle diagram, distance across the red segment is represented by 'd'.
Congruent segments- are segments that have the same length. Symbol ≅
AB ≅ CD
AB ≅ CD
Construction- a way of creating a figure that is more precise than a sketch.
The diagram shows construction of a bisector.
The diagram shows construction of a bisector.
In order for you to say that a point B is between two points A and C, all three of the points must lie on the same line, and AB + BC = AC.
In the diagram, AB + BC =AC
In the diagram, AB + BC =AC
Midpoint- the midpoint M a segment AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of segment AB, then AM = MB.
The midpoint of the segment on the left is highlighted in red.
The midpoint of the segment on the left is highlighted in red.
Bisect- to divide into two congruent parts.
This line bisects the segment.
Segment Bisector- any ray, segment, or line that intersects a segment at its midpoint.
The constructed segment bisector is perfectly dividing the segment in two.
This line bisects the segment.
Segment Bisector- any ray, segment, or line that intersects a segment at its midpoint.
The constructed segment bisector is perfectly dividing the segment in two.
Lesson 7 Terms
Angle- a figure formed by two rays, or sides, with a common endpoint called the vertex. Notated with <
The diagram is formed by two rays, and has a common vertex, making it an angle.
The diagram is formed by two rays, and has a common vertex, making it an angle.
Interior Of An Angle- the set of all points between the sides of the angle.
D is in the interior of <ABC.
Exterior- all of the points outside the angle.
A is in the exterior of <DBC
D is in the interior of <ABC.
Exterior- all of the points outside the angle.
A is in the exterior of <DBC
Measure- for an angle, given in degrees.
The protractor shown can help in finding the measure of an angle.
The protractor shown can help in finding the measure of an angle.
Degree- 1/360 of a circle. Notated with °
The diagram show the full 360° of a circle.
The diagram show the full 360° of a circle.
Acute Angle- an angle measuring greater than 0° and less than 90°.
The angle is acute, because it is less than 90°, and more than 0°.
The angle is acute, because it is less than 90°, and more than 0°.
Right Angle- an angle measuring 90°.
m<JKL = 90°
m<JKL = 90°
Obtuse Angle- an angle measuring greater than 90° and less than 180°.
The angle is obtuse because it is more than 90° and less than 180°.
The angle is obtuse because it is more than 90° and less than 180°.
Straight Angle- an angle formed by two opposite rays and measures 180°.
m<ABC = 180°
m<ABC = 180°
Congruent Angles- angles that have the same measure.
The angles on the left are congruent, because 60° = 60°.
The angles on the left are congruent, because 60° = 60°.
Angle Bisector- a ray that divides an angle into two congruent angles.
Ray BD bisects <ABC.
Ray BD bisects <ABC.
Adjacent Angles- two angles in the same plane with a common vertex and a common side, but no common interior points.
a and b are adjacent.
a and b are adjacent.
Linear Pair- a linear pair of angles is a pair of adjacent angles whose non-common sides are opposite rays.
x = 90°
x = 90°
Complementary Angles- two angles whose measures have a sum of 90°.
m<AOC + m<COB = 90°
m<AOC + m<COB = 90°
Supplementary Angles- two angles whose measures have a sum of 180°.
30° + 150° = 180°
30° + 150° = 180°
Vertical Angles- two nonadjacent angles formed by two intersecting lines.
Angles 1 and 4 are vertical angles.
Angles 1 and 4 are vertical angles.
Lesson 8 Terms
Theorem- any statement that you can prove.
Pythagorus Pythagorus's theorem states a^2 + b^2 = c^2.
Pythagorus Pythagorus's theorem states a^2 + b^2 = c^2.
Two-column Proof- a type of proof where the statements and corresponding reasons are listed in two columns with the statements in the left column and the reasons in the right column.
Flowchart Proof- a proof that uses boxes and arrows to show the structure of a proof.
The flow chart's boxes are connected by arrows, forming the order of the proofs.
The flow chart's boxes are connected by arrows, forming the order of the proofs.
Paragraph Proof- a proof where the statements and reasons are presented as sentences in a paragraph.