Reasoning and Proof Review Questions


 Basil Wright
 1 years ago
 Views:
Transcription
1 1 Reasoning and Proof Review Questions Inductive Reasoning from Patterns 1. What is the next term in the pattern: 1, 4, 9, 16, 25, 36, 49...? (a) 81 (b) 64 (c) 121 (d) What is the next term in the pattern 2, 6, 18, 54, 162? (a) 486 (b) 324 (c) Complete the sequence: 1, 2, 4, (a) 32 (b) 16 (c) 16 (d) What is the next number in the sequence: 243, 81, 27, 9... (a) 0 (b) 3 (c) 1 (d) 1/3 5. Examples of inductive reasoning include. (a) Visual patterns (b) Number patterns (c) Both A, B 6. Deductive reasoning is the process of drawing conclusions based on examples and patterns. ( True/False ) 7. Inductive reasoning differs from deductive reasoning in that a general conclusion is drawn by observing specific examples. ( True/False ) 8. Inductive reasoning is the opposite of induction or inductive logic. ( True/False )
2 2 Conjectures and Counterexamples 1. are conjectures disproven through counterexample. (a) Pseudo conjectures (b) False conjectures (c) Proxy conjectures 2. An example that disproves a conjecture is a (a) A counterexample (b) Pseudo conjectures (c) Proxy conjectures 3. Find the best counterexample from the given options to show that the following conjecture is false: the difference of two integers is less than either integer. (a) Difference between 7 and 8 (b) Difference between 9 and 2 (c) Difference between 3 and 4 4. Which of the following proves that a conjecture is true? (a) Deductive reasoning (b) Counterexample (c) Both A, B 5. All shapes with four sides of the same length are squares. ( True/False ) 6. The counterexample to the statement, "All students are lazy," is, "Any hard working student." ( True/False ) 7. If the product of two numbers is even, then the two numbers must be even. The counterexample to this statement are 7 and 4. ( True/False ) 8. 2 is a counterexample to the statement, "All prime numbers are odd numbers." ( True/False ) Deductive Reasoning 1. Determine the right conclusion from the following statements: I. A shape that has more than 2 sides is a polygon. II. A regular polygon s sides and angles are all congruent. III. An equilateral triangle has 3 congruent sides and 3 congruent angles.
3 3 (a) All triangles are polygons. (b) An equilateral triangle is a regular polygon. (c) A rectangle with sides 2, 2, 4, and 4 is not a regular polygon. (d) All of the above can be concluded. 2. Using the two equations, determine the relationship between p and q. 2p = p + 3 II. Q 5 2 = 1. Therefore: (a) (b) (c) (d) q > p p > q p = q None 3. Which of the following laws would be used to draw a logical conclusion from the statements: If you are not in London, then you can t be on the bridge. Ben is in London. (a) Law of Contrapositive (b) Law of Detachment (c) Both A, B 4. Under which of the following laws is a conclusion reached by combining the hypothesis of one statement with the conclusion of another? (a) Law of detachment (b) Law of syllogism (c) Law of induction 5. Determine the conclusion from the following statements: If it is snowing, then I wear a cap. I am not wearing a cap. (a) It is snowing (b) It is not snowing (c) It is winter 6. The difference between inductive and deductive arguments lies in the strength of the evidence that the premises do not provide for the conclusion, and have nothing to do with the content or subject matter of the argument. ( True/False ) 7. P, Q, and R, are collinear points. Q is equidistant from P and R. Therefore, Q must be the midpoint between P and R. ( True/False ) 8. In deductive reasoning, a specific conclusion can be drawn from a general truth. ( True/False )
4 4 IfThen Statements 1. If a = b and b = c, then (a) (b) (c) a > c a < c a = c (d) None o f the above 2. Two lines are perpendicular lines if they intersect to form a. (a) Obtuse angle (b) Right Angle (c) Supplementary angle 3. A conclusion is the result of a(n). (a) Hypothesis (b) Premise (c) Argument 4. If x = 10, then 10x is 100. (a) TRUE (b) FALSE (c) You should meditate 5. If a rectangle has four equal side lengths, then it is a. (a) Square (b) Rectangle (c) Polygon 6. Give the hypothesis and conclusion of the following statement: If x = 29, then x 9 = 20. (a) No conclusion (b) The statement is ambiguous. (c) Hypothesis: x = 29; Conclusion: x  9 = If x = 4, then 3x = 12. ( True/False ) 8. A triangle has three sides. ( True/False )
5 5 Converse, Inverse, and Contrapositive 1. Consider the statement, "If two angles are congruent, then they have the same measure". What is the converse of the statement? (a) If two angles have the same measure, then they are congruent. (b) If two angles are not congruent, then they do not have the same measure. (c) If two angles do not have the same measure, then they are not congruent. 2. In the statement, "If it rains, then they will cancel school",[u+009d] what is the hypothesis? (a) They will cancel School (b) It rains (c) They will 3. Consider the statement, "If it rains, then I do not go outside." Which of the following could be a logical conclusion that we can draw from this statement? (a) If it does not rain, then I can go fishing (b) If I do not go fishing, then it rains (c) If I go fishing, then it does not rain 4. For any statement where A implies B, notb implies nota. (a) Always (b) Not always (c) Sometimes 5. Consider the statement, "All blue objects have color." Its inverse is. (a) If an object has color, then it is blue (b) There exists a blue object that does not have the properties of color (c) If an object is not blue, then it does not have color 6. "If it is cold, then I will wear my woolen clothes." The converse of the preceding statement is, "If I wear my woolen clothes, then it is not cold." ( True/False ) 7. "If something is a bat, then it is a mammal." The contrapositive to this statement is, "If something is a mammal, then it is not a bat." ( True/False ) 8. The converse and inverse of a statement are always true. ( True/False )
6 6 Properties of Equality and Congruence 1. If DE = ED then it is a. (a) Reflexive property of equality (b) Symmetric property of equality (c) Addition Property of equality 2. According to the Right Angle Congruence Theorem, all angles are congruent. (a) Right (b) Acute (c) Obtuse 3. If 3b = 18, then 3b 3 = 18 3 or b = 6. What property makes the statement true? (a) Division Property of Equality (b) Substitution property of equality (c) Symmetric property of equality (d) Addition Property of equality 4. If two angles form a linear pair, then they are: (a) Right angles (b) Obtuse angles (c) Supplementery angles 5. In a triangle, the largest angle is across from the. (a) Shortest side (b) Longest side (c) Shortest angle 6. The sum of interior angles of triangle is. (a) 90 degrees (b) 45 degrees (c) 180 degrees 7. If a = b, then b = a is a symmetric property. ( True/False ) 8. If a quadrilateral is a parallelogram, then the opposite sides are perpendicular. ( True/False )
7 7 TwoColumn Proofs 1. We need to explicitly state that BD = BD. This idea that something is congruent to itself is called the: (a) Reflexive property of equality (b) Symmetric property of equality (c) Addition Property of equality (d) Transitive property 2. In higherlevel mathematics, are usually written in paragraph form. (a) Proofs (b) Hypothesis (c) Axioms 3. If 3x + 4 = 16 then x =. (a) 12 (b) 4 (c) 13 (d) 3 4. In parallelogram ABCD, angle ABD is congruent to angle BDC because if we have parallel lines and a transversal, we know that: (a) Alternate interior angles are congruent (b) sameside interior angles are congruent (c) corresponding angles are congruent (d) exterior angles are congruent 5. The Vertical Angles Theorem states that vertical angles are congruent. ( True/False ) 6. A statement that is proved is often called a hypothesis. ( True/False ) 7. If a = b, and a + b = 10, and a = 5, then b = 10. ( True/False ) 8. To clarify and emphasize the effectiveness of an argument in geometry, a twocolumn approach has a list of statements and the corresponding reasons supporting the truth of these statements is often adapted. ( True/False )
Geometry  Chapter 2 Review
Name: Class: Date: Geometry  Chapter 2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine if the conjecture is valid by the Law of Syllogism.
More informationChapter 1: Essentials of Geometry
Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,
More informationVocabulary. Term Page Definition Clarifying Example. biconditional statement. conclusion. conditional statement. conjecture.
CHAPTER Vocabulary The table contains important vocabulary terms from Chapter. As you work through the chapter, fill in the page number, definition, and a clarifying example. biconditional statement conclusion
More informationIn the examples above, you used a process called inductive reasoning to continue the pattern. Inductive reasoning is.
Lesson 7 Inductive ing 1. I CAN understand what inductive reasoning is and its importance in geometry 3. I CAN show that a conditional statement is false by finding a counterexample Can you find the next
More information2.) 5000, 1000, 200, 40, 3.) 1, 12, 123, 1234, 4.) 1, 4, 9, 16, 25, Draw the next figure in the sequence. 5.)
Chapter 2 Geometry Notes 2.1/2.2 Patterns and Inductive Reasoning and Conditional Statements Inductive reasoning: looking at numbers and determining the next one Conjecture: sometimes thought of as an
More informationGEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
More informationconditional statement conclusion Vocabulary Flash Cards Chapter 2 (p. 66) Chapter 2 (p. 69) Chapter 2 (p. 66) Chapter 2 (p. 76)
biconditional statement conclusion Chapter 2 (p. 69) conditional statement conjecture Chapter 2 (p. 76) contrapositive converse Chapter 2 (p. 67) Chapter 2 (p. 67) counterexample deductive reasoning Chapter
More informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationEx 1: For points A, B, and C, AB = 10, BC = 8, and AC = 5. Make a conjecture and draw a figure to illustrate your conjecture.
Geometry 21 Inductive Reasoning and Conjecturing A. Definitions 1. A conjecture is an guess. 2. Looking at several specific situations to arrive at a is called inductive reasoning. Ex 1: For points A,
More information55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.
Geometry Core Semester 1 Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit
More informationGeometry Chapter 2: Geometric Reasoning Lesson 1: Using Inductive Reasoning to Make Conjectures Inductive Reasoning:
Geometry Chapter 2: Geometric Reasoning Lesson 1: Using Inductive Reasoning to Make Conjectures Inductive Reasoning: Conjecture: Advantages: can draw conclusions from limited information helps us to organize
More informationChapter Three. Parallel Lines and Planes
Chapter Three Parallel Lines and Planes Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately
More informationGeometry: 2.12.3 Notes
Geometry: 2.12.3 Notes NAME 2.1 Be able to write all types of conditional statements. Date: Define Vocabulary: conditional statement ifthen form hypothesis conclusion negation converse inverse contrapositive
More informationGeometry Essential Curriculum
Geometry Essential Curriculum Unit I: Fundamental Concepts and Patterns in Geometry Goal: The student will demonstrate the ability to use the fundamental concepts of geometry including the definitions
More informationContent Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade
Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources
More information1.1 Identify Points, Lines, and Planes
1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms  These words do not have formal definitions, but there is agreement aboutwhat they mean.
More informationGeometry Unit 1. Basics of Geometry
Geometry Unit 1 Basics of Geometry Using inductive reasoning  Looking for patterns and making conjectures is part of a process called inductive reasoning Conjecture an unproven statement that is based
More information14 add 3 to preceding number 35 add 2, then 4, then 6,...
Geometry Definitions, Postulates, and Theorems hapter 2: Reasoning and Proof Section 2.1: Use Inductive Reasoning Standards: 1.0 Students demonstrate understanding by identifying and giving examples of
More informationGeometry Chapter 1 Vocabulary. coordinate  The real number that corresponds to a point on a line.
Chapter 1 Vocabulary coordinate  The real number that corresponds to a point on a line. point  Has no dimension. It is usually represented by a small dot. bisect  To divide into two congruent parts.
More informationCoordinate Coplanar Distance Formula Midpoint Formula
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand twodimensional coordinate systems to
More informationState the assumption you would make to start an indirect proof of each statement.
1. State the assumption you would make to start an indirect proof of each statement. Identify the conclusion you wish to prove. The assumption is that this conclusion is false. 2. is a scalene triangle.
More informationCCGPS UNIT 6 Semester 2 COORDINATE ALGEBRA Page 1 of 33. Connecting Algebra and Geometry Through Coordinates
GPS UNIT 6 Semester 2 OORDINTE LGER Page 1 of 33 onnecting lgebra and Geometry Through oordinates Name: Date: M912.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example,
More information#2. Isosceles Triangle Theorem says that If a triangle is isosceles, then its BASE ANGLES are congruent.
1 Geometry Proofs Reference Sheet Here are some of the properties that we might use in our proofs today: #1. Definition of Isosceles Triangle says that If a triangle is isosceles then TWO or more sides
More informationName: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work
Name: _ 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work 1. An equilateral triangle always has three 60 interior angles. 2. A line segment
More informationCOURSE OVERVIEW. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved
COURSE OVERVIEW The geometry course is centered on the beliefs that The ability to construct a valid argument is the basis of logical communication, in both mathematics and the realworld. There is a need
More informationShow all work for credit. Attach paper as needed to keep work neat & organized.
Geometry Semester 1 Review Part 2 Name Show all work for credit. Attach paper as needed to keep work neat & organized. Determine the reflectional (# of lines and draw them in) and rotational symmetry (order
More informationDefinitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
More informationPROVING STATEMENTS IN GEOMETRY
CHAPTER PROVING STATEMENTS IN GEOMETRY After proposing 23 definitions, Euclid listed five postulates and five common notions. These definitions, postulates, and common notions provided the foundation for
More informationFinal Review Geometry A Fall Semester
Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over
More informationMATHEMATICS SAMPLE. 1.1 Writing Conditional, Converse, and Inverse Statements and Determining the Truth Value of these Statements
MATHEMATICS SAMPLE Copyright 2011 by North Farm Enterprises, LLC, 2405 North Hillfield Rd. Layton, Utah 84041 Chapter 1 1.1 Writing Conditional, Converse, and Inverse Statements and Determining the Truth
More informationLesson 13: Proofs in Geometry
211 Lesson 13: Proofs in Geometry Beginning with this lesson and continuing for the next few lessons, we will explore the role of proofs and counterexamples in geometry. To begin, recall the Pythagorean
More informationA summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:
summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of midpoint and segment bisector M If a line intersects another line segment
More informationINDEX. Arc Addition Postulate,
# 3060 right triangle, 441442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent
More informationDistance, Midpoint, and Pythagorean Theorem
Geometry, Quarter 1, Unit 1.1 Distance, Midpoint, and Pythagorean Theorem Overview Number of instructional days: 8 (1 day = 45 minutes) Content to be learned Find distance and midpoint. (2 days) Identify
More informationGeometry. Unit 6. Quadrilaterals. Unit 6
Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections
More informationPatterns and Inductive Reasoning
21 Reteaching Patterns and Inductive Reasoning Inductive reasoning is a type of reasoning in which you look at a pattern and then make some type of prediction based on the pattern. These predictions are
More informationMiddle Grades Mathematics 5 9
Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from realworld situations. 2. Apply problemsolving strategies
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
More information1.2 Informal Geometry
1.2 Informal Geometry Mathematical System: (xiomatic System) Undefined terms, concepts: Point, line, plane, space Straightness of a line, flatness of a plane point lies in the interior or the exterior
More information**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.
Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:
More informationPicture. Right Triangle. Acute Triangle. Obtuse Triangle
Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from
More informationPicture. Right Triangle. Acute Triangle. Obtuse Triangle
Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from
More informationCurriculum Map by Block Geometry Mapping for Math Block Testing 20072008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 20072008 Pre s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)
More informationGeometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures.
Geometry: Unit 1 Vocabulary 1.1 Undefined terms Cannot be defined by using other figures. Point A specific location. It has no dimension and is represented by a dot. Line Plane A connected straight path.
More informationSemester Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Are O, N, and P collinear? If so, name the line on which they lie. O N M P a. No,
More information1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.
Quadrilaterals  Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals  Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,
More informationGeometry Review (1 st semester)
NAME HOUR Geometry Review (1 st semester) 1) The midpoint of XY is Z. If XY = n and XZ = n + 15, what is YZ? A) 18 B) 6 C) 45 D) 90 ) What is RS? A) 5 B) 56 C) D) 70 ) Which is an obtuse angle? A) PQR
More information4. Prove the above theorem. 5. Prove the above theorem. 9. Prove the above corollary. 10. Prove the above theorem.
14 Perpendicularity and Angle Congruence Definition (acute angle, right angle, obtuse angle, supplementary angles, complementary angles) An acute angle is an angle whose measure is less than 90. A right
More informationFoundations of Geometry 1: Points, Lines, Segments, Angles
Chapter 3 Foundations of Geometry 1: Points, Lines, Segments, Angles 3.1 An Introduction to Proof Syllogism: The abstract form is: 1. All A is B. 2. X is A 3. X is B Example: Let s think about an example.
More informationalternate interior angles
alternate interior angles two nonadjacent angles that lie on the opposite sides of a transversal between two lines that the transversal intersects (a description of the location of the angles); alternate
More informationAlgebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
More information(subject) (predicate) Example identify the hypothesis and the conclusion and write it in ifthen form:
Name Date Conditional Practice Conditional Statement logical statement with 2 parts (subject) (predicate) Can be written in Ifthen form If, then Example identify the hypothesis and the conclusion and
More informationTeacher Annotated Edition Study Notebook
Teacher Annotated Edition Study Notebook Copyright by The McGrawHill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be
More informationLecture 24: Saccheri Quadrilaterals
Lecture 24: Saccheri Quadrilaterals 24.1 Saccheri Quadrilaterals Definition In a protractor geometry, we call a quadrilateral ABCD a Saccheri quadrilateral, denoted S ABCD, if A and D are right angles
More information2.1. Inductive Reasoning EXAMPLE A
CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers
More information1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
More informationIntermediate Math Circles October 10, 2012 Geometry I: Angles
Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,
More informationObjectives. 22 Conditional Statements
Geometry Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90. F 2. All perfectsquare numbers are positive. 3. Every prime number is odd. F 4. Any three
More informationPolygons are figures created from segments that do not intersect at any points other than their endpoints.
Unit #5 Lesson #1: Polygons and Their Angles. Polygons are figures created from segments that do not intersect at any points other than their endpoints. A polygon is convex if all of the interior angles
More informationChapter 1. Reasoning in Geometry. Section 11 Inductive Reasoning
Chapter 1 Reasoning in Geometry Section 11 Inductive Reasoning Inductive Reasoning = Conjecture = Make a conjecture from the following information. 1. Eric was driving his friends to school when his car
More informationChapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More information1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?
1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional
More informationLine. A straight path that continues forever in both directions.
Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A
More information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More informationMath 311 Test III, Spring 2013 (with solutions)
Math 311 Test III, Spring 2013 (with solutions) Dr Holmes April 25, 2013 It is extremely likely that there are mistakes in the solutions given! Please call them to my attention if you find them. This exam
More informationChapters 4 and 5 Notes: Quadrilaterals and Similar Triangles
Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles IMPORTANT TERMS AND DEFINITIONS parallelogram rectangle square rhombus A quadrilateral is a polygon that has four sides. A parallelogram is
More informationPOTENTIAL REASONS: Definition of Congruence:
Sec 6 CC Geometry Triangle Pros Name: POTENTIAL REASONS: Definition Congruence: Having the exact same size and shape and there by having the exact same measures. Definition Midpoint: The point that divides
More information41 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.
ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.
More informationGeometry Topic 5: Conditional statements and converses page 1 Student Activity Sheet 5.1; use with Overview
Geometry Topic 5: Conditional statements and converses page 1 Student Activity Sheet 5.1; use with Overview 1. REVIEW Complete this geometric proof by writing a reason to justify each statement. Given:
More informationStudent Name: Teacher: Date: District: MiamiDade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1
Student Name: Teacher: Date: District: MiamiDade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the
More information65 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.
ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 3. PROOF Write a twocolumn proof to prove that if ABCD is a rhombus with diagonal. 1. If, find. A rhombus is a parallelogram with all
More informationGeometry Chapter 5 Review Relationships Within Triangles. 1. A midsegment of a triangle is a segment that connects the of two sides.
Geometry Chapter 5 Review Relationships Within Triangles Name: SECTION 5.1: Midsegments of Triangles 1. A midsegment of a triangle is a segment that connects the of two sides. A midsegment is to the third
More information0810ge. Geometry Regents Exam 0810
0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationGeometry Credit Recovery
Geometry Credit Recovery COURSE DESCRIPTION: This is a comprehensive course featuring geometric terms and processes, logic, and problem solving. Topics include parallel line and planes, congruent triangles,
More information23 Conditional Statements. Identify the hypothesis and conclusion of each conditional statement. 1. If today is Friday, then tomorrow is Saturday.
Identify the hypothesis and conclusion of each conditional statement. 1. If today is Friday, then tomorrow is Saturday. 2. Hypothesis: Today is Friday. Conclusion: Tomorrow is Saturday. Hypothesis: 2x
More informationGeometry Chapter 2 Study Guide
Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies
More information65 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.
ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram
More informationSelected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationINFORMATION FOR TEACHERS
INFORMATION FOR TEACHERS The math behind DragonBox Elements  explore the elements of geometry  Includes exercises and topics for discussion General information DragonBox Elements Teaches geometry through
More informationparallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect
parallel lines lines that stay same distance from each other forever and never intersect perpendicular lines lines that cross at a point and form 90 angles intersecting lines vertices lines that cross
More informationGEOMETRY FINAL EXAM REVIEW
GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.
More informationConjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence  a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
More informationGEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!
GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationA convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.
hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.
More informationGeometry: Euclidean. Through a given external point there is at most one line parallel to a
Geometry: Euclidean MATH 3120, Spring 2016 The proofs of theorems below can be proven using the SMSG postulates and the neutral geometry theorems provided in the previous section. In the SMSG axiom list,
More information11.3 Curves, Polygons and Symmetry
11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon
More informationPROPERTIES OF TRIANGLES AND QUADRILATERALS
Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 21 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS
More information1. point, line, and plane 2a. always 2b. always 2c. sometimes 2d. always 3. 1 4. 3 5. 1 6. 1 7a. True 7b. True 7c. True 7d. True 7e. True 8.
1. point, line, and plane 2a. always 2b. always 2c. sometimes 2d. always 3. 1 4. 3 5. 1 6. 1 7a. True 7b. True 7c. True 7d. True 7e. True 8. 3 and 13 9. a 4, c 26 10. 8 11. 20 12. 130 13 12 14. 10 15.
More informationQuadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid
Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,
More informationGrade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in twodimensional shapes and determine if angles are greater than or less than a right angle (obtuse
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationPerformance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will
Performance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will discover and prove the relationship between the triangles
More information2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
More informationGeometry Chapter 5 Relationships Within Triangles
Objectives: Section 5.1 Section 5.2 Section 5.3 Section 5.4 Section 5.5 To use properties of midsegments to solve problems. To use properties of perpendicular bisectors and angle bisectors. To identify
More informationCopyright 2014 Edmentum  All rights reserved. 04/01/2014 Cheryl Shelton 10 th Grade Geometry Theorems Given: Prove: Proof: Statements Reasons
Study Island Copyright 2014 Edmentum  All rights reserved. Generation Date: 04/01/2014 Generated By: Cheryl Shelton Title: 10 th Grade Geometry Theorems 1. Given: g h Prove: 1 and 2 are supplementary
More informationBlue Pelican Geometry Theorem Proofs
Blue Pelican Geometry Theorem Proofs Copyright 2013 by Charles E. Cook; Refugio, Tx (All rights reserved) Table of contents Geometry Theorem Proofs The theorems listed here are but a few of the total in
More information