M 1312 Section Trapezoids


 Paulina Taylor
 2 years ago
 Views:
Transcription
1 M 1312 Section Trapezoids Definition: trapezoid is a quadrilateral with exactly two parallel sides. Parts of a trapezoid: Base Leg Leg Leg Base Base Base Leg Isosceles Trapezoid: Every trapezoid contains two pairs of consecutive angles that are supplementary. Definition: n altitude of a trapezoid is a segment drawn from any point on one of the parallel sides (base) perpendicular to the opposite side (the other base). n infinite number of altitudes may be drawn in a trapezoid.
2 M 1312 Section Definition: median of a trapezoid is the segment that joins the midpoints of the nonparallel sides (legs). Median Median Theorem: The median of a trapezoid is parallel to each base and the length of the median equals onehalf the sum of the lengths of the two bases. M Definition: n isosceles trapezoid is a trapezoid in which the legs (nonparallel sides) are congruent. n isosceles trapezoid features some special properties not found in all trapezoids. Theorem 4.4.1: The base angles of an isosceles trapezoid are congruent. Theorem 4.4.2: The diagonals of an isosceles trapezoid are congruent.
3 M 1312 Section Properties of Isosceles Trapezoid 1. The legs are congruent. 2. The bases are parallel. 3. The lower base angles of an isosceles trapezoid are congruent. 4. The upper base angles of an isosceles trapezoid are congruent. 5. The lower base angle is supplementary to any upper base angle. 6. The diagonals of an isosceles trapezoid are congruent. 7. The median is parallel to the base. 8. The length of the median equals onehalf the sum of the lengths of the two bases. Proving that Trapezoid is isosceles 1. If legs of a trapezoid are congruent then it is an isosceles trapezoid. 2. If two base angles of a trapezoid are congruent, then it is an isosceles trapezoid. 3. If the diagonals of a trapezoid are congruent, then it is an isosceles trapezoid. Example 1: Given the trapezoid HLJK H L J K If the m J 65 and the m K 95, the measure of angles H and L.
4 M 1312 Section Popper 12 question 1: Given a kite BD. is the perpendicular bisector of BD. Find B if B = 5 and the perimeter of the kite is 24. D O B. 5 B D 14 E. None of these Example 2: Use Isosceles Trapezoid BD with length of D = B. D B ll D B a. mdb = 75. Find the md. b. = 40. Find BD. c. If m 6x 25 and m B 8x 15, find the measures of angle and D.
5 M 1312 Section Definition: m altitude is a line segment from one vertex of one base of the trapezoid and perpendicular to the opposite base. Popper 12 question 2: In parallelogram BD (not shown), the diagonals have the lengths = 7 and BD = 9. Which pair of angles have greater measures? and D B. B and. and D. and B E. None of these Theorem 4.4.3: The length of the median of a trapezoid equals onehalf the sum of the bases. 1 m b 1 b 2 2 Example 3: Find the missing measures of the given trapezoid. B 7 I a. mird b. YR c. DR D X Y R 75 3 d.
6 M 1312 Section Example 4: HJKL is an isosceles trapezoid with bases HJ and LK, and median RS. Use the given information to solve each problem. a. LK = 30 HJ = 42 find RS L R S K b. RS = 17 HJ = 14 find LK H J c. RS = x + 5 HJ + LK = 4x + 6 find RS Example 5: Given WXYZ is a trapezoid with WX ZY, MN is the median W X M N Z Y a. If WX =19 and ZY = 31, find MN b. If WX = 4x 7, MN = 2x + 10 and ZY = 2x + 1, find x and the lengths of WX, MN and ZY.
7 M 1312 Section SUMMRY HRTS: Special Diagonals re lways Diagonals lways Bisect Quadrilateral ongruent Perpendicular Each Other ngles Parallelogram No No Yes No Rectangle Yes No Yes No Rhombus No Yes Yes Yes Square Yes Yes Yes Yes Trapezoid No No No No Isosceles Trapezoid Yes No No No There is an excellent chart in your book on page 205. Use for Popper 12 questions 35: HJKL is an isosceles trapezoid with bases HJ and LK, and median RS. Use the given information to solve each problem. L K R S H J Popper 12 question 3: If LK =30 and HJ = 42 then find RS.. RS =36 B RS = 20. RS =7 D. RS =2 E. None of these Popper 12 question 4: If RS =17 and HJ = 14, find LK.. RS =36 B RS = 20. RS =7 D. RS =2 E. None of these Popper 12 question 5: If RS = x + 5 and HJ + LK = 4x + 6 find RS.. RS =36 B RS = 20. RS =7 D. RS =2 E. None of these
8 M 1312 Section Solutions to Popper 10 Solutions for Popper 10: Use for Popper 10 question 1 and question 2: H E 4x + 2 x + 8 G Popper 10 question 1: Find in parallelogram EFGH.. B.. D. D. None of these F Popper 10 question 2: Find in parallelogram EFGH.. B.. D. D. None of these Popper 10 question 3: ssume that X, Y, and Z are midpoints of the sides of RST. If RS = 28, ST = 12, and RT = 18, find XY.. XY=6 B. XY = 9. XY = 14 D. XY = 24 E. None of these Use for Popper 10 questions 4 and 5: Given : B =18, D = 9, E = 8 and B = 18 and D and E are midpoints.
9 M 1312 Section E D B Popper 10 question 4: Find the length of DE.. DE = 8 B. DE = 15. DE = 18 D. DE = 16 E None of these Popper 10 question 5: Find the length of E.. E = 8 B. E = 15. E = 18 D. E = 16 E None of these D y E x B 30
(n = # of sides) One interior angle:
6.1 What is a Polygon? Regular Polygon Polygon Formulas: (n = # of sides) One interior angle: 180(n 2) n Sum of the interior angles of a polygon = 180 (n  2) Sum of the exterior angles of a polygon =
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 informationSum of the interior angles of a nsided Polygon = (n2) 180
5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a nsided Polygon = (n2) 180 What you need to know: How to use the formula
More informationObjectives. Cabri Jr. Tools
Activity 24 Angle Bisectors and Medians of Quadrilaterals Objectives To investigate the properties of quadrilaterals formed by angle bisectors of a given quadrilateral To investigate the properties of
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 informationAlgebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More informationGeometry 81 Angles of Polygons
. Sum of Measures of Interior ngles Geometry 81 ngles of Polygons 1. Interior angles  The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.
More information8.1 Find Angle Measures in Polygons
8.1 Find Angle Measures in Polygons Obj.: To find angle measures in polygons. Key Vocabulary Diagonal  A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Polygon ABCDE has two
More informationUnit 3: Triangle Bisectors and Quadrilaterals
Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties
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 information*Students will answer the following warmup questions: Name each of the following figures. Can each figure have more than one name? Why or why not?
Student Lesson Plan Topic: Quadrilateral Properties and Relationships Subject Area/Content: General Education Geometry/Integrated II Course: 10 th Grade Time: 260 minute classes Lesson Objectives: 1.
More informationUnit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period
Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,
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 informationFinal Review Problems Geometry AC Name
Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x6. Find the measure of the angles. State the theorem(s) that support your equation.
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 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 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 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 informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
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 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 informationHonors Packet on. Polygons, Quadrilaterals, and Special Parallelograms
Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386
More information(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units
1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units
More informationLesson 28: Properties of Parallelograms
Student Outcomes Students complete proofs that incorporate properties of parallelograms. Lesson Notes Throughout this module, we have seen the theme of building new facts with the use of established ones.
More information2006 ACTM STATE GEOMETRY EXAM
2006 TM STT GOMTRY XM In each of the following you are to choose the best (most correct) answer and mark the corresponding letter on the answer sheet provided. The figures are not necessarily drawn to
More informationGiven: ABCD is a rhombus. Prove: ABCD is a parallelogram.
Given: is a rhombus. Prove: is a parallelogram. 1. &. 1. Property of a rhombus. 2.. 2. Reflexive axiom. 3.. 3. SSS. + o ( + ) =180 4.. 4. Interior angle sum for a triangle. 5.. 5. PT + o ( + ) =180 6..
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 informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
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 informationLesson 3.1 Duplicating Segments and Angles
Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each
More informationSpecial case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2
Geometry Chapter 11/12 Review Shape: Rectangle Formula A= Base x Height Special case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2 Height = 6 Base = 8 Area = 8 x 6
More informationCONJECTURES  Discovering Geometry. Chapter 2
CONJECTURES  Discovering Geometry Chapter C1 Linear Pair Conjecture  If two angles form a linear pair, then the measures of the angles add up to 180. C Vertical Angles Conjecture  If two angles are
More informationQuadrilaterals Unit Review
Name: Class: Date: Quadrilaterals Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) In which polygon does the sum of the measures of
More informationGeometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24
Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: ctivity 24 esources: Springoard Geometry Unit Overview In this unit, students will study formal definitions of basic figures,
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 informationBASIC GEOMETRY GLOSSARY
BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that
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 informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfdprep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
More informationChapters 6 and 7 Notes: Circles, Locus and Concurrence
Chapters 6 and 7 Notes: Circles, Locus and Concurrence IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of
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 informationCh 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and Angles [and Triangles]
h 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and ngles [and Triangles] Warm up: Directions: Draw the following as accurately as possible. Pay attention to any problems you may be having.
More information10.1: Areas of Parallelograms and Triangles
10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a
More information1) Perpendicular bisector 2) Angle bisector of a line segment
1) Perpendicular bisector 2) ngle bisector of a line segment 3) line parallel to a given line through a point not on the line by copying a corresponding angle. 1 line perpendicular to a given line through
More informationQUADRILATERALS CHAPTER
HPTER QURILTERLS Euclid s fifth postulate was often considered to be a flaw in his development of geometry. Girolamo Saccheri (1667 1733) was convinced that by the application of rigorous logical reasoning,
More informationArea. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
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 informationSituation: Proving Quadrilaterals in the Coordinate Plane
Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra
More informationQUADRILATERALS CHAPTER 8. (A) Main Concepts and Results
CHAPTER 8 QUADRILATERALS (A) Main Concepts and Results Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square. Sum of
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 informationPolygons in the Coordinate Plane. isosceles 2. X 2 4
Name lass ate 67 Practice Form G Polgons in the oordinate Plane etermine whether k is scalene, isosceles, or equilateral. 1. isosceles. scalene 3. scalene. isosceles What is the most precise classification
More informationChapter 6 Notes: Circles
Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment
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 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 informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 111: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More informationA = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height
Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side
More informationCHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms
CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 17 HW: Pgs: 810 DAY 2: (62) Pgs:
More informationSOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses
CHAPTER SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY For the review sessions, I will try to post some of the solved homework since I find that at this age both taking notes and proofs are still a burgeoning
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 informationIsosceles triangles. Key Words: Isosceles triangle, midpoint, median, angle bisectors, perpendicular bisectors
Isosceles triangles Lesson Summary: Students will investigate the properties of isosceles triangles. Angle bisectors, perpendicular bisectors, midpoints, and medians are also examined in this lesson. 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 informationb. Create a graph to show how far Maggie and Mike can travel based on the chart above.
Final Exam Review 1. Find the midpoint, the distance and the slope between (4,2) and (5, 3) 2. Jacinta hangs a picture 15 inches from the left side of a wall. How far from the edge of the wall should
More informationCumulative Test. 161 Holt Geometry. Name Date Class
Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2
More informationThe Parallelogram REMEMBER A parallelogram is a quadrilateral with opposite sides parallel. It has many special properties.
ame: Date: The Parallelogram REMEMBER A parallelogram is a quadrilateral with opposite sides parallel. It has many special properties. If you are given parallelogram ABCD then: Property Meaning (1) opposite
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 informationChapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
More informationTABLE OF CONTENTS. Free resource from Commercial redistribution prohibited. Understanding Geometry Table of Contents
Understanding Geometry Table of Contents TABLE OF CONTENTS Why Use This Book...ii Teaching Suggestions...vi About the Author...vi Student Introduction...vii Dedication...viii Chapter 1 Fundamentals of
More informationLEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.
Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the
More information*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.
Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More informationABC is the triangle with vertices at points A, B and C
Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry  symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the
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 informationUnit 8 Geometry QUADRILATERALS. NAME Period
Unit 8 Geometry QUADRILATERALS NAME Period 1 A little background Polygon is the generic term for a closed figure with any number of sides. Depending on the number, the first part of the word Poly is replaced
More informationGeo  CH6 Practice Test
Geo  H6 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measure of each exterior angle of a regular decagon. a. 45 c. 18 b. 22.5
More informationName Geometry Exam Review #1: Constructions and Vocab
Name Geometry Exam Review #1: Constructions and Vocab Copy an angle: 1. Place your compass on A, make any arc. Label the intersections of the arc and the sides of the angle B and C. 2. Compass on A, make
More informationQuadrilateral Geometry. Varignon s Theorem I. Proof 10/21/2011 S C. MA 341 Topics in Geometry Lecture 19
Quadrilateral Geometry MA 341 Topics in Geometry Lecture 19 Varignon s Theorem I The quadrilateral formed by joining the midpoints of consecutive sides of any quadrilateral is a parallelogram. PQRS is
More information63 Tests for Parallelograms. Determine whether each quadrilateral is a parallelogram. Justify your answer.
1. Determine whether each quadrilateral is a Justify your answer. 3. KITES Charmaine is building the kite shown below. She wants to be sure that the string around her frame forms a parallelogram before
More informationMath 531, Exam 1 Information.
Math 531, Exam 1 Information. 9/21/11, LC 310, 9:059:55. Exam 1 will be based on: Sections 1A  1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)
More informationCircle Name: Radius: Diameter: Chord: Secant:
12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane
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 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 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 informationQuadrilaterals GETTING READY FOR INSTRUCTION
Quadrilaterals / Mathematics Unit: 11 Lesson: 01 Duration: 7 days Lesson Synopsis: In this lesson students explore properties of quadrilaterals in a variety of ways including concrete modeling, patty paper
More informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
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 informationNCERT. The coordinates of the midpoint of the line segment joining the points P (x 1. which is non zero unless the points A, B and C are collinear.
COORDINATE GEOMETRY CHAPTER 7 (A) Main Concepts and Results Distance Formula, Section Formula, Area of a Triangle. The distance between two points P (x 1 ) and Q (x, y ) is ( x x ) + ( y y ) 1 1 The distance
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 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 informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationof one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
2901 Clint Moore Road #319, Boca Raton, FL 33496 Office: (561) 4592058 Mobile: (949) 5108153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:
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 informationYou can use the postulates below to prove several theorems.
Using Area Formulas You can use the postulates below to prove several theorems. AREA POSTULATES Postulate Area of a Square Postulate The area of a square is the square of the length of its side, or s.
More informationThe Triangle and its Properties
THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter 6 6.1 INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three
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 informationHigher Geometry Problems
Higher Geometry Problems ( Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationQuadrilaterals. Definition
Quadrilaterals Definition A quadrilateral is a foursided closed figure in a plane that meets the following conditions: Each side has its endpoints in common with an endpoint of two adjacent sides. Consecutive
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
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 information