Mrs. Eakes Geometry Vocabulary 1st Semester Exam – Flashcards
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POINT Why are point, line and plane considered "undefined terms"?
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They are only explained using examples and descriptions
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LINE Describe a line as completely as possible.
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Made up of points and has no thickness or width. It extends infinitely in both directions.
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PLANE What are the ways to name a plane?
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A capital script letter or by the letters naming three noncollinear points
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COPLANAR Points that do not lie in the same plane are said to be ____________.
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Noncoplanar
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SPACE Define.
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a boundless, three-dimensional set of all points
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SEGMENT Explain the difference between lines and line segments.
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Lines cant be measured because they extend infinitely in both directions but line segments have two endpoints and can be measured.
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PRECISION A measurement should be precise to within ______ unit of measure.
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0.5
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CONSTRUCTION What are the geometric constructions tools?
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Pencil, straightedge, compass
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MIDPOINT If X is the midpoint of segment AB, what can be stated about segments AX and BX?
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segment AX is congruent to segment BX
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BISECTOR How is a midpoint different from a segment bisector?
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A midpoint is a point on the segment; whereas a segment bisector is a segment, line, or plane that intersects the segment at the midpoint
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DEGREE How much of a turn around a circle is a degree?
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1/360 th
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RAY Describe a ray
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it is part of a line and it has one endpoint but it continues infinetely in one direction
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ANGLE What forms an angle?
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2 noncollinear rays that have a common endpoint
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INTERIOR Into what 3 distinct parts does an angle divide a plane?
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Points on the angle, points in the interior of the angle, or points in the exterior of the angle
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EXTERIOR Are all points either in the interior or exterior of an angle?
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No, they could be on the angle
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ACUTE What is the degree measure of an acute angle?
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Less than 90 degrees
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VERTICAL What forms vertical angles? Sketch a pair of vertical angles
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Intersecting lines
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LINEAR PAIR Since the sum of a linear pair is 180 degrees, does that mean that all supplementary angles are linear pairs?
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No. Supplementary angles do have a sum of 180 degrees but they do not have to be adjacent angles
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COMPLEMENTARY If an angle is measured as x, what is the value of its complement?
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90-x
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SUPPLEMENTARY Draw and label an adjacent pair and a non-adjacent supplementary pair
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Degree measures will vary but the sum will always be 180
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POLYGON A polygon _________ is a figure whose sides are all ___________.
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closed, segments
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CONVEX What is required for a polygon to be convex?
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If lines containing each side are drawn and none of the lines contain points in the interior of the figure
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REGULAR How would you find the length of a side of a regular decagon if the perimeter is 120 centimeters?
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120 divided by 10 equal sides = 12 centimeters per side
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PERIMETER The Pentagon building in Arlington, VA is so named because of its 5 congruent sides. Find the perimeter of the outside of the Pentagon if one side is 921 feet long
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921 (5) = 4605 feet
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AREA Define
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The number of square units needed to cover a surface
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CONJECTURE Define. What type of reasoning leads to a conjecture?
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A conjecture is an educated guess based on known information. A conjecture is formed from inductive reasoning
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INDUCTIVE REASONING What is the other type of reasoning?
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Deductive
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COUNTEREXAMPLE How many counterexamples does it take to prove a conjecture is not true?
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1
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STATEMENT What is the difference between a statement and a conjecture?
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A conjecture is an educated guess, whereas a statement is known to be either true or false
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COMPOUND STATEMENT What are the 2 types of mathematical compound statements in logic?
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conjunction and disjunction
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TRUTH VALUE How many possibilities are there for a truth value?
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Two, true or false
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NEGATION What is the symbol? The negation of a statement has the opposite _________ and the opposite _____ _______.
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~ Meaning, truth value
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CONJUNCTION Symbolically write the conjunction of "not p and q"
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~p^q
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DISJUNCTION What is the word that joins 2 or more statements to create a disjunction?
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or
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TRUTH TABLE When is a conjunction true? When is a disjunction true?
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A conjunction is true only when both statements are true. A disjunction is true unless both statements are false
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CONDITIONAL STATEMENT In what form is a conditional statement written?
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"If-then" form
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HYPOTHESIS Which part of a conditional statement is the hypothesis?
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The "if" part
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CONCLUSION Write the conclusion to the following statement: "If points A, B, C ine on line m.....
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Then they are collinear
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CONVERSE Writing the converse of a conditional statement means exchanging the ___________ and __________.
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hypothesis and conclusion
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INVERSE Writing the inverse of a conditional statement means _________ both the hypothesis and conclusion.
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negating
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CONTRAPOSITIVE Explain in your own words the contrapositive of a conditional statement.
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Exchange the hypothesis and conclusion and then negate each one (inverse of the converse)
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LOGICALLY EQUIVALENT Write 2 statements that are logically equivalent
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Conditional and contrapositive OR converse and inverse (statements with the same truth value)
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DEDUCTIVE REASONING How is deductive reasoning different from inductive reasoning?
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Inductive uses previous examples to make a conjecture, whereas deductive reasoning uses facts, definitions, and properties and theorems to form a logical conclusion
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LAW OF DETACHMENT This law uses ______ conditional statements to draw conclusions
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true
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LAW OF SYLLOGISM This law is similar to the __________ property of equality
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transitive
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POSTULATE What is a postulate?
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a statement that is accepted as true
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AXIOM What is another name for an axiom?
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postulate
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THEOREM What is a theorem? In what way can a theorem be used?
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A statement of conjecture that has been shown to be true. It can be used to justify that other statements are true
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PROOF What is a proof? What can support a statement in a proof?
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A logical argument in which each statement you make is supported. Definitions, postulates, properties of equality, and theorems can be used to support statements
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PARAGRAPH PROOF What is the difference between paragraph proofs and 2-column proofs?
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Paragraph proofs involve a written paragraph to explain why a conjecture is true. Two-column proofs list step by step statements that lead to the true result and each statement is supported by a definition, postulate, property or theorem
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INFORMAL PROOF What type of proof is considered informal?
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Paragraph proof
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DEDUCTIVE ARGUMENT What is a deductive argument? What are the steps in a deductive argument?
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A group of algebraic steps used to solve problems. Algebraic properties of equality: reflexive, symmetric, transitive, addition, subtraction, multiplication, division, substitution, and distributive
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TWO-COLUMN PROOF What are the 2 parts of a two-column proof?
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Statements and reasons
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FORMAL PROOF What type of proof is considered formal?
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two-column proof
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PARALLEL LINES If lines are coplanar but not parallel, what type of lines are they?
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Intersecting
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PARALLEL PLANES In a rectangular prism, what planes are parallel to each other?
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top and bottom Front and back Left and right sides
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SKEW Define
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Lines that do not intersect and are not coplanar
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CONSECUTIVE INTERIOR ANGLES What is another name for consecutive interior angles? What is true about their measurements?
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same side interior angles supplementary
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VERTICAL ANGLES Define
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Non-adjacent, congruent angles formed by intersecting lines
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SLOPE Define
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The steepness of a graph line; the ratio of the vertical change (the rise) to the horizontal change (the run)
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RATE OF CHANGE What is a synonym for rate of change in relation to linear equations?
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slope
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EQUIDISTANT Define Give an example involving a segment
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A point is equidistant from two figures if the point is the same distance form each figure EXAMPLE- Midpoint
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OBTUSE TRIANGLE What types of angles are the 3 angles of an obtuse triangle?
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One is obtuse and the other two are acute
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RIGHT TRIANGLE What term(s) describes the two non-right angles of a right triangle?
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acute and complementary
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EQUIANGULAR TRIANGLE Explain why each angle of an equiangular triangle is 60 degrees
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The sum of the angles of a triangle is 180 degrees and 180 divided by 3 equal angles is 60 degrees each angle
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EQUILATERAL TRIANGLE An equilateral triangle is isosceles. Sometime, Never, or Always?
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Always because an isosceles triangle has at least 2 congruent sides and a equilateral triangle has 3 congruent sides
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COROLLARY Define
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A statement that can be easily proved using a theorem is called a corollary of that theorem
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CONGRUENT TRIANGLES What must be true for triangles to be congruent?
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All 3 pairs of corresponding angles are congruent and all 3 pairs of corresponding sides are congruent
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CONGRUENCE TRANSFORMATIONS What are the 3 types of transformations that maintain congruence between triangles?
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Reflection (flip) Rotation (turn) Translation (slide)
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INCLUDED ANGLE Which congruence postulate involves an included angle?
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SAS
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BASE ANGLES If the vertex angle of an isosceles triangle is 70 degrees, what is the measure of each base angle?
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55 because 180-70=110 110 divided by 2 equal base angles = 55 each
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COORDINATE PROOF Which coordinate represents the east/west value of a location on the earth?
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the x coordinate; the y would be the north/south value
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PERPENDICULAR BISECTOR What 2 things does a perpendicular bisector do to the side of the triangle that it intersects?
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Divides the side into 2 congruent segments and forms a right angle with the side
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ANGLE BISECTOR Any point on the angle bisector is ____________ from the sides of the angle
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equidistant
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CONCURRENT LINES Define
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3 or more lines that intersect at a common point
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POINT OF CONCURRENCY Name the point of concurrency for the following: 1. perpendicular bisector 2. angle bisector 3. median 4. altitude
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1. circumcenter 2. incenter 3. centroid 4. orthocenter
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CIRCUMCENTER How do you find the coordinates of the circumcenter?
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Solver a system of equations from any 2 of the 3 perpendicular biscetors
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MEDIAN Where are the endpoints of a median located?
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One endpoint is a vertex of the triangle. The other endpoint is the midpoint of the side opposite the vertex
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CENTRIOD The centroid is located ________ of the distance from the vertex to the midpoint of the side opposite the vertex
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2/3
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ALTITUDE How are a perpendicular bisector and an altitude similar? How are they different?
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They are similar in that they both form a right angle with the side of the triangle they intersect. They are different in that the perpendicular bisector always intersects the side at the midpoint but not necessarily so for the altitude
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ORTHOCENTER An orthocenter is located outside the triangle. Sometimes, Always, or Never?
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Sometimes
