Name: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester


 Aubrie Mosley
 2 years ago
 Views:
Transcription
1 Name: Chapter 4 Guided Notes: Congruent Triangles Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester
2 CH. 4 Guided Notes, page Apply Triangle Sum Properties triangle polygon sides vertices Classifying Triangles by Sides scalene triangle isosceles triangle equilateral triangle
3 Classifying Triangles by Angles CH. 4 Guided Notes, page 3 acute triangle obtuse triangle right triangle equiangular triangle interior angles exterior angles 4.1 Triangle Sum The sum of the measures of the interior angles of a triangle is 180. auxiliary lines 4.2 Exterior Angle The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. corollary to a theorem Corollary to the Triangle Sum The acute angles of a right triangle are complementary.
4 4.2 Apply Congruence and Triangles CH. 4 Guided Notes, page 4 congruent figures corresponding parts 4.3 Third Angles Reflexive Property of Congruent Triangles Symmetric Property of Congruent Triangles Transitive Property of Congruent Triangles If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Properties of Congruent Triangles 4.4 Properties of Congruent Triangles For any triangle ABC, If If! ABC "! ABC.! ABC "! DEF, then DEF "! ABC!.! ABC "! DEF and DEF "! JKL then! ABC "! JKL.!,
5 4.3 Prove Triangles Congruent by SSS CH. 4 Guided Notes, page 5 Postulate 19 SideSideSide (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
6 CH. 4 Guided Notes, page Prove Triangles Congruent by SAS and HL included angle Postulate 20 SideAngle Side (SAS) Congruence Postulate right triangles If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. 1. legs 2. hypotenuse 3. side opposite 4. sides adjacent 4.5 HypotenuseLeg (HL) Congruence If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
7 CH. 4 Guided Notes, page Prove Triangles Congruent by ASA and AAS included side Postulate 21 AngleSideAngle (ASA) Congruence Postulate 4.6 AngleAngleSide (AAS) Congruence If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent. If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the two triangles are congruent. flow proof More Right Triangle Congruence s LegLeg (LL) Congruence If the legs of two right triangles are congruent, then the triangles are congruent. 1. SAS (included angle) AngleLeg (AL) Congruence If an angle and a leg of a right triangle are congruent to an angle and a leg of a second right triangle, then the triangles are congruent. 1. AAS (nonincluded side) 2. ASA (included side) HypotenuseAngle (HA) Congruence If an angle and the hypotenuse of a right triangle are congruent to an angle and the hypotenuse of a second right triangle, then the triangles are congruent. 1. AAS (nonincluded side)
8 4.6 Use Congruent Triangles CH. 4 Guided Notes, page 8 congruent triangles Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if their corresponding parts are congruent. This is also known as the Corresponding Parts of Congruent Triangles are Congruent. To show that a pair of corresponding parts of two triangles are congruent: 1. Prove the two triangles are congruent. 2. Use the definition of congruent triangles (CPCTC) to show the corresponding parts are congruent. What can we say about SSA and AAA? SSA SSA cannot be used as a proof of congruent triangles. See page 247. AAA AAA cannot be used as a proof of congruent triangles. AAA only proves the two triangles to be similar.
9 CH. 4 Guided Notes, page Use Isosceles and Equilateral Triangles 5 Vertex Angle parts of an isosceles triangle 6 Legs 7 Base 8 Base Angles 4.7 Base Angles 4.8 Converse of Base Angles Corollary to the Base Angles Corollary to the Converse of Base Angles If two sides of a triangle are congruent, then the angles opposite them are congruent. If two angles of a triangle are congruent, then the sides opposite them are congruent. If a triangle is equilateral, then it is equiangular. If a triangle is equiangular, then it is equilateral.
Triangles can be classified by angles and sides. Write a good definition of each term and provide a sketch: Classify triangles by angles:
Chapter 4: Congruent Triangles A. 41 Classifying Triangles Identify and classify triangles by angles. Identify and classify triangles by sides. Triangles appear often in construction. Roofs sit atop a
More informationChapter 4: Congruent Triangles
Name: Chapter 4: Congruent Triangles Guided Notes Geometry Fall Semester 4.1 Apply Triangle Sum Properties CH. 4 Guided Notes, page 2 Term Definition Example triangle polygon sides vertices Classifying
More informationChapter 5.1 and 5.2 Triangles
Chapter 5.1 and 5.2 Triangles Students will classify triangles. Students will define and use the Angle Sum Theorem. A triangle is formed when three noncollinear points are connected by segments. Each
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 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 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 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 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 information4.1 Apply Triangle Sum Properties
4.1 Apply Triangle Sum Properties Obj.: Classify triangles and find measures of their angles. Key Vocabulary Triangle  A triangle is a polygon w it h three sid es. A t r ian gle w it h ver t ices A, B,
More informationMath 3372College Geometry
Math 3372College Geometry Yi Wang, Ph.D., Assistant Professor Department of Mathematics Fairmont State University Fairmont, West Virginia Fall, 2004 Fairmont, West Virginia Copyright 2004, Yi Wang Contents
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 informationGEOMETRY: TRIANGLES COMMON MISTAKES
GEOMETRY: TRIANGLES COMMON MISTAKES 1 GeometryClassifying Triangles How Triangles are Classified TypesTriangles are classified by Angles or Sides By Angles Obtuse Trianglestriangles with one obtuse
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 informationUnit 8: Congruent and Similar Triangles Lesson 8.1 Apply Congruence and Triangles Lesson 4.2 from textbook
Unit 8: Congruent and Similar Triangles Lesson 8.1 Apply Congruence and Triangles Lesson 4.2 from textbook Objectives Identify congruent figures and corresponding parts of closed plane figures. Prove that
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 informationHow Do You Measure a Triangle? Examples
How Do You Measure a Triangle? Examples 1. A triangle is a threesided polygon. A polygon is a closed figure in a plane that is made up of segments called sides that intersect only at their endpoints,
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 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 informationName: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: _ ate: _ I: SSS Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Given the lengths marked on the figure and that bisects E, use SSS to explain
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 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 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 informationA polygon with five sides is a pentagon. A polygon with six sides is a hexagon.
Triangles: polygon is a closed figure on a plane bounded by (straight) line segments as its sides. Where the two sides of a polygon intersect is called a vertex of the polygon. polygon with three sides
More informationMath 330A Class Drills All content copyright October 2010 by Mark Barsamian
Math 330A Class Drills All content copyright October 2010 by Mark Barsamian When viewing the PDF version of this document, click on a title to go to the Class Drill. Drill for Section 1.3.1: Theorems about
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 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 informationPARALLEL LINES CHAPTER
HPTR 9 HPTR TL OF ONTNTS 91 Proving Lines Parallel 92 Properties of Parallel Lines 93 Parallel Lines in the oordinate Plane 94 The Sum of the Measures of the ngles of a Triangle 95 Proving Triangles
More informationNeutral Geometry. Chapter Neutral Geometry
Neutral Geometry Chapter 4.14.4 Neutral Geometry Geometry without the Parallel Postulate Undefined terms point, line, distance, halfplane, angle measure Axioms Existence Postulate (points) Incidence
More informationPOTENTIAL REASONS: Definition of Congruence: Definition of Midpoint: Definition of Angle Bisector:
Sec 1.6 CC Geometry Triangle Proofs Name: POTENTIAL REASONS: Definition of Congruence: Having the exact same size and shape and there by having the exact same measures. Definition of Midpoint: The point
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 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 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 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 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 informationChapter 4 Study guide
Name: Class: Date: ID: A Chapter 4 Study guide Numeric Response 1. An isosceles triangle has a perimeter of 50 in. The congruent sides measure (2x + 3) cm. The length of the third side is 4x cm. What is
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 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 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 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. 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 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 informationCLIL MultiKey lesson plan
LESSON PLAN Subject: Mathematics Topic: Triangle Age of students: 16 Language level: B1, B2 Time: 4560 min Contents aims: After completing the lesson, the student will be able to: Classify and compare
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 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 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 informationOn Geometric Proofs: Base angles of an isosceles trapezoid are equal Perpendicular bisectors of a triangle meet at a common point
On Geometric Proofs: Base angles of an isosceles trapezoid are equal Perpendicular bisectors of a triangle meet at a common point Before demonstrating the above proofs, we should review what sort of geometric
More informationChapter Four. Congruent Triangles
Chapter Four Congruent Triangles 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 apply
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 informationThe Six Trigonometric Functions
CHAPTER 1 The Six Trigonometric Functions Copyright Cengage Learning. All rights reserved. SECTION 1.1 Angles, Degrees, and Special Triangles Copyright Cengage Learning. All rights reserved. Learning Objectives
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 informationGeo, Chap 4 Practice Test, EV Ver 1
Class: Date: Geo, Chap 4 Practice Test, EV Ver 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (43) In each pair of triangles, parts are congruent as
More informationClassify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.
ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. One angle of the triangle measures 90, so it is a right angle. Since the triangle has a
More informationG E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY. Notes & Study Guide
G E O M E T R Y CHAPTER 9 RIGHT TRIANGLES AND TRIGONOMETRY Notes & Study Guide 2 TABLE OF CONTENTS SIMILAR RIGHT TRIANGLES... 3 THE PYTHAGOREAN THEOREM... 4 SPECIAL RIGHT TRIANGLES... 5 TRIGONOMETRIC RATIOS...
More informationSu.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)
MA.912.G.2 Geometry: Standard 2: Polygons  Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures
More information2. Sketch and label two different isosceles triangles with perimeter 4a + b. 3. Sketch an isosceles acute triangle with base AC and vertex angle B.
Section 1.5 Triangles Notes Goal of the lesson: Explore the properties of triangles using Geometer s Sketchpad Define and classify triangles and their related parts Practice writing more definitions Learn
More informationANALYTIC GEOMETRY. Study Guide. Georgia EndOfCourse Tests
ANALYTIC GEOMETRY Study Guide Georgia EndOfCourse Tests TABLE OF CONTENTS INTRODUCTION...5 HOW TO USE THE STUDY GUIDE...6 OVERVIEW OF THE EOCT...8 PREPARING FOR THE EOCT...9 Study Skills...9 Time Management...10
More informationThe Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry
The Protractor Postulate and the SAS Axiom Chapter 3.43.7 The Axioms of Plane Geometry The Protractor Postulate and Angle Measure The Protractor Postulate (p51) defines the measure of an angle (denoted
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 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 informationUnit 7  Test. Name: Class: Date: 1. If BCDE is congruent to OPQR, then DE is congruent to?. A. PQ B. OR C. OP D. QR 2. BAC?
Class: Date: Unit 7  Test 1. If BCDE is congruent to OPQR, then DE is congruent to?. A. PQ B. OR C. OP D. QR 2. BAC? A. PNM B. NPM C. NMP D. MNP 3. Given QRS TUV, QS = 3v + 2, and TV = 7v 6, find the
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 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 informationMaths Toolkit Teacher s notes
Angles turtle Year 7 Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles. Use a ruler and protractor
More informationSession 2 Triangles and Quadrilaterals
Session 2 Triangles and Quadrilaterals Key Terms for This Session Previously Introduced altitude perpendicular bisector New in This Session acute triangle congruent congruent triangles equilateral triangle
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 informationProof Case #1 CD AE. AE is the altitude to BC. Given: CD is the altitude to AB. Prove: ABC is isosceles
Proof Case #1 B Given: CD is the altitude to AB AE is the altitude to BC CD AE Prove: ABC is isosceles D E A C Proof Case # 2 Given: AB CD DC bisects ADE Prove: ABD is isosceles Proof Case #3 Given: 1
More informationTImath.com. Geometry. Triangle Sides & Angles
Triangle Sides & Angles ID: 8792 Time required 40 minutes Activity Overview In this activity, students will explore side and angle relationships in a triangle. First, students will discover where the longest
More informationSpoonsAlgebra Style
SpoonsAlgebra Style The Object Be the first player to hold a set of four cards with the same solution. What You'll Need A set of four matching solution cards per player. If playing with less than 13 players
More informationand the angle measuring 39 are congruent.
Find the measures of each numbered angle 1 The sum of the measures of the angles of a triangle is 180 Let x be the measure of unknown angle in the figure 2 The sum of the measures of the angles of a triangle
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 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 informationSHAPE, SPACE AND MEASURES
SHAPE, SPACE AND MEASURES Pupils should be taught to: Use accurately the vocabulary, notation and labelling conventions for lines, angles and shapes; distinguish between conventions, facts, definitions
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 informationGeometry: Classifying, Identifying, and Constructing Triangles
Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral
More informationAnalysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 550 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website
Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 550 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1 NCTM Standards Addressed Problem Solving Geometry Algebra
More informationCRLS Mathematics Department Geometry Curriculum Map/Pacing Guide. CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page of 6 2 77.5 Unit : Tools of 5 9 Totals Always Include 2 blocks for Review & Test Activity binder, District Google How do you find length, area? 2 What are the basic tools
More informationFormal Geometry S1 (#2215)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following course: Formal Geometry S1 (#2215)
More informationNCERT. not to be republished TRIANGLES UNIT 6. (A) Main Concepts and Results
UNIT 6 TRIANGLES (A) Main Concepts and Results The six elements of a triangle are its three angles and the three sides. The line segment joining a vertex of a triangle to the mid point of its opposite
More informationClassifying Triangles. Lesson 1 VOCABULARY TARGET. right angle. acute angle. obtuse angle congruent isosceles. I can classify triangles.
Classifying Lesson 1 VOCABULARY TARGET acute angle right angle obtuse angle congruent isosceles scalene Venn diagram equilateral I can classify triangles. You classify many things around you. For example,
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 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 informationGeometry, Final Review Packet
Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a
More informationInscribed Angle Theorem and Its Applications
: Student Outcomes Prove the inscribed angle theorem: The measure of a central angle is twice the measure of any inscribed angle that intercepts the same arc as the central angle. Recognize and use different
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. 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 informationTriangles. Triangle. a. What are other names for triangle ABC?
Triangles Triangle A triangle is a closed figure in a plane consisting of three segments called sides. Any two sides intersect in exactly one point called a vertex. A triangle is named using the capital
More informationGeometry in a Nutshell
Geometry in a Nutshell Henry Liu, 26 November 2007 This short handout is a list of some of the very basic ideas and results in pure geometry. Draw your own diagrams with a pencil, ruler and compass where
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 information1 of 69 Boardworks Ltd 2004
1 of 69 2 of 69 Intersecting lines 3 of 69 Vertically opposite angles When two lines intersect, two pairs of vertically opposite angles are formed. a d b c a = c and b = d Vertically opposite angles are
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 Concepts ANGLES Angles acute right obtuse straight protractor Complementary angles Supplementary angles Adjacent angles Linear pairs
Gemetry Cncepts ANGLES Angles can be classified as: acute (less than 9 ) right (equal t 9, a square crner) btuse (greater than 9 but less than 18 ) straight (equal t 18, a straight line). Angles are measured
More informationLogic Rule 0 No unstated assumptions may be used in a proof. Logic Rule 1 Allowable justifications.
Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and NonEuclidean Geometries, 4th Ed by Marvin Jay Greenberg (Revised: 18 Feb 2011) Logic Rule 0 No unstated assumptions may be
More informationChapter 4. Outline of chapter. 1. More standard geometry (interior and exterior angles, etc.) 3. Statements equivalent to the parallel postulate
Chapter 4 Outline of chapter 1. More standard geometry (interior and exterior angles, etc.) 2. Measurement (degrees and centimeters) 3. Statements equivalent to the parallel postulate 4. Saccheri and Lambert
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 informationCopyright 2015 Edmentum All rights reserved.
Triangles 1. A triangle has 2 angles that each measure 71. A. isosceles triangle B. right triangle C. obtuse triangle D. equiangular triangle Copyright 2015 Edmentum All rights reserved. 2. Directions:
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 informationI Theorem 4.1 Triangle Sum Theorem
NAME For use with pages 194201 _ DATE Classify triangles by their sides and angles and find angie measures in triangles A triangle is a figure formed by three segments joining three noncollinear points.
More informationCircles in Triangles. This problem gives you the chance to: use algebra to explore a geometric situation
Circles in Triangles This problem gives you the chance to: use algebra to explore a geometric situation A This diagram shows a circle that just touches the sides of a right triangle whose sides are 3 units,
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 informationSolutions to inclass problems
Solutions to inclass problems College Geometry Spring 2016 Theorem 3.1.7. If l and m are two distinct, nonparallel lines, then there exists exactly one point P such that P lies on both l and m. Proof.
More information