Geometry Definitions, Postulates, and Theorems. Chapter 4: Congruent Triangles. Section 4.1: Apply Triangle Sum Properties
|
|
- Louisa Collins
- 6 years ago
- Views:
Transcription
1 Geometry efinitions, Postulates, and Theorems Key hapter 4: ongruent Triangles Section 4.1: pply Triangle Sum Properties Standards: 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. Triangle polygon formed by three segments joining three non-collinear points. triangle can be classified by its sides and then by its angles. *lassifying Triangles by Sides: Scalene Triangle triangle with no congruent sides. Leg ase ngle Isosceles Triangle triangle with at least two congruent sides. Vertex ngle Legs The congruent sides of an isosceles triangle, when only two sides are congruent. ase Leg ase ngle ase The third side (non-congruent side) of an isosceles triangle. quilateral Triangle triangle with three congruent sides. *lassifying Triangles by ngles: 45 cute Triangle triangle with three acute angles Leg Hypotenuse Right Triangle triangle with one right angle. Legs The sides that form the right angle. Hypotenuse The side opposite the right angle. Leg Obtuse Triangle triangle with one obtuse angle. 50 quiangular Triangle triangle with three congruent acute angles. (over)
2 x. lassify the triangles by their sides and angles. a) b) c) 120 Isosceles Obtuse quilateral quiangular/cute Scalene Right Vertex (plural: vertices) ach of the three points joining the sides of a triangle. djacent Sides of an ngle Two sides that share a common vertex. Opposite Side from an ngle The side that does not form the angle. Interior angles When the sides of a triangle are extended, additional angles are formed. The original angles are the interior angles. xterior angles When the sides of a triangle are extended, additional angles are formed. The angles that form linear pairs with the interior angles are the exterior angles. ***Theorem 4.1 Triangle Sum Theorem The sum of the measures of the three interior angles of a triangle is m = 67 0 ***Theorem 4.2 xterior ngle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles m 1 = orollary To The Triangle Sum Theorem The acute angles of a right triangle are complementary (add up to equal 90 ). Y X Z (over)
3 x. triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. ( 5,4), (2,6), (4, 1) Yes, right triangle Isosceles x. ind the value of x and y. x. ind the value of x. Then classify the triangle by its angles. Then classify the triangle by its angles x Linear Pair x y (2x-18) x. ind the angle measures of the numbered angles x. ind the values of x and y. y 0 x
4 Section 4.2: pply ongruence and Triangles Standards: 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. Two geometric figures are congruent if they have exactly the same size and shape, like placing one figure perfectly onto another figure. Y V ongruent igures ll the parts of one figure are congruent to the corresponding parts of the other figure. In congruent polygons, the corresponding sides and the corresponding angles are congruent. X W ongruence When writing a congruence statement for two polygons, always list the corresponding vertices in the same order! x. GIVN: orresponding ngles orresponding Sides x. Write a congruency statement. x. JKHL. ind the value of x and y. T L 9 cm J Q S x 3 cm R 86 0 (5y 12) 0 K P U H ***Theorem 4.3 Third ngle Theorem I two angles of one triangle are congruent to two angles of another triangle, THN, the third angles are also congruent. x. x G H K I J (over)
5 ***Theorem 4.4 Properties of ongruent Triangles Reflexive Property of ongruent Triangles or any triangle :. Symmetric Property of ongruent Triangles I, then. Transitive Property of ongruent Triangles I, and JKL, then JKL. x. ind the values of x and y. ( 8 y 0 0 x 2 ) ( 6x y)
6 Section 4.3: Prove Triangles ongruent by SSS Standards: 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. ***Side-Side-Side (SSS) ongruence Postulate I three sides of one triangle are congruent to three sides of a second triangle, THN the two triangles are congruent. *Information about the angles is not needed. If Side, Side, and Side, then by. x. Is the congruence statement true? xplain your reasoning. WXY YZW x. Is the congruence statement true? xplain your reasoning. KJL MJL X K L Y W Z J M x. Write a proof. Given: Prove:, Reflexive (over)
7 Structural Support diagonal support added to a figure helps make the figure stable. The diagonal support forms triangles with fixed side lengths. y the SSS ongruence Postulate, these triangles cannot change shape and so the figure is stable. x. etermine whether the figure is stable. xplain your answer. a) b) c) Given:,, Given: Prove: W X Z Y WX YX Z is the midpoint of WY Prove: WXZ YXZ 1.,, 1. Given 1. WX YX 1. Given Z is the midpoint of WY 2. = = WZ ZY 3. + = 4. + = 4. Substitution = ef. of ongruent Segments SSS
8 Section 4.4: Prove Triangles ongruent by SS and HL Standards: 4.0 Students prove basic theorems involving congruence and similarity. 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. ***Side-ngle-Side (SS) ongruence Postulate I two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, THN the two triangles are congruent. If Side, ngle, and Side, then by. x. o you have enough information to prove the triangles are congruent by SS? a) b) x. Write a proof. Given: Prove:, Vertical ngles are ongruent (over)
9 x. Write a proof. M Given: Prove: P, M P M MP P lines form rights angles 3. M MP Reflexive Property 5. M MP 5. Right Triangles: Legs The sides adjacent to the right angle. Hypotenuse The side opposite the right angle. ***Hypotenuse-Leg (HL) ongruence Theorem I the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, THN the two triangles are congruent. x. Write a proof. Given: Prove:, lines form rights angles Reflexive Property 5. 5.
10 Section 4.5: Prove Triangles ongruent by S and S Standards: 4.0 Students prove basic theorems involving congruence and similarity. 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. ***ngle-side-ngle (S) ongruence Postulate I two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, THN the two triangles are congruent. If ngle, Side, and ngle, then by. ***ngle-ngle-side (S) ongruence Postulate I two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, THN the two triangles are congruent. If ngle, ngle, and Side, then by. x. Is it possible to prove the triangles are congruent? If so, state the postulate or theorem used. a) / b) / c) / d) / (over)
11 x. Write a proof. X Given: WZ bisects XZY and XWY Prove: WZX WZY Z W Y efinition of an angle bisector 3. ZW ZW WZX WZY 4. x. Write a proof. Given:,, M is the midpoint of Prove: M M M efinition of a midpoint 3. M M 3.
12 Section 4.6: Use ongruent Triangles Standards: 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. ***orresponding Parts of ongruent Triangles are ongruent (.P..T..) 1. Prove two triangles are congruent with SSS, SS, HL, S, or S. 2. Then, conclude that the corresponding parts of these congruent triangles are congruent as well. The triangles below are congruent by SS. Since the triangles are congruent, we know that: Y X Z x. Write a proof. H J Given: Prove: HJ II LK, JK II HL LHJ JKL L K lternate Interior ngles are ongruent 3. JL JL LHJ JKL LHJ JKL 5. x. Write a proof. M R Given: MS II TR, MS TR Prove: is the midpoint of MT S T lternate Interior ngles are ongruent 3. MS TR PT 5. is the midpoint of MT 5. (over)
13 x. Write a proof. P Given: MP bisects Prove: LP NP LMN, LM NM N L M 2. NMP LMP Reflexive Property 4. NMP LMP LP NP 5. x. Which triangles can you show are congruent in order to prove the statement? What postulate or theorem would you use? a) b) SW TY S W X Y T
14 Section 4.7: Use Isosceles and quilateral Triangles Standards: 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. Vertex ngle Legs The two congruent sides in an isosceles triangle. Leg Leg Vertex ngle The angle formed by the legs in an isosceles triangle. ase The third side of the isosceles triangle. ase ngle ase ase ngles The two angles adjacent to the base in an isosceles triangle. ase ngle ***Theorem 4.7 ase ngles Theorem I two sides of a triangle are congruent, THN the angles opposite them are congruent. 30 x ***Theorem 4.8 onverse of ase ngles Theorem I two angles of a triangle are congruent, THN the sides opposite them are congruent. 2x-4 2x+2 x+5 orollary To ase ngles Theorem I a triangle is equilateral, THN it is equiangular. orollary to the onverse of ase ngles Theorem I a triangle is equiangular, THN it is equilateral.
15 Section 4.8: Perform ongruence Transformations Standards: 22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. Transformation n operation that moves or changes a geometric figure in some way to produce a new figure. Image The new figure produced. Pre-Image Image ' *Three Types of Transformations: ' ' ' ' Translation Moves every point of a figure the same distance in the same direction. Translate down 6 Translate right 10 ' Reflection Uses a line of reflection to create a mirror image of the original figure. Rotation Turns a figure about a fixed point, called the center of rotation. Rotate 90 degrees clockwise ongruence Transformation hanges the position of the figure without changing its size or shape. Translate igure In The oordinate Plane Moving an object a given distance right or left and up or down. y *oordinate Notation for a Translation You can describe a translation by the notation ( x, y) ( x a, y b) which shows that each point ( x, y) of a figure is translated horizontally a units and vertically b units x. igure has the vertices ( 4,2), ( 2,5), ( 1,1), and ( 3, 1). Sketch and its image after the translation ( x, y) ( x 5, y 2). Right 5 own 2 ' ' ' ' x (over)
16 Usually Reflect igure In The oordinate Plane The line of reflection is always the x-axis or the y-axis. y *oordinate Notation for a Reflection Reflection in the x-axis: ( x, y) ( x, y) Multiply the y-coordinate by -1. Reflection in the y-axis: ( x, y) ( x, y) Multiply the x-coordinate by -1. x x. Use a reflection in the x-axis to draw the other half of the figure. Rotate igure In The oordinate Plane The center of rotation is the origin. The direction of rotation can be either clockwise or counterclockwise. The angle of rotation is formed by rays drawn from the center of rotation through corresponding points on the original figure and its image clockwise rotation 60 0 counterclockwise rotation x. Graph PQ and RS. Tell whether RS is a rotation of PQ about the origin. If so, give the angle and direction of rotation. y P a) P ( 2,6), Q(5,1), R(6, 1), S(1, 2) Q x b) P ( 4,2), Q(3,3), R( 2,4), S( 3,3) S R
CHAPTER # 4 CONGRUENT TRIANGLES
HPTER # 4 ONGRUENT TRINGLES In this chapter we address three ig IES: 1) lassify triangles by sides and angles 2) Prove that triangles are congruent 3) Use coordinate geometry to investigate triangle relationships
More informationGeometry Unit 4a - Notes Triangle Relationships
Geometry Unit 4a - Notes Triangle Relationships This unit is broken into two parts, 4a & 4b. test should be given following each part. Triangle - a figure formed by three segments joining three noncollinear
More informationThere are three ways to classify triangles based on sides
Unit 4 Notes: Triangles 4-1 Triangle ngle-sum Theorem ngle review, label each angle with the correct classification: Triangle a polygon with three sides. There are two ways to classify triangles: by angles
More informationClassify each triangle by its side lengths as equilateral, isosceles, or scalene. (Note: Give two classifications in Exercise 13.)
hapter 4 ongruent Triangles 4.2 and 4.9 lassifying Triangles and Isosceles, and quilateral Triangles. Match the letter of the figure to the correct vocabulary word in xercises 1 4. 1. right triangle 2.
More informationCh 4 Review Problems pp #7 36, 48,51,52 due MONDAY 12/12
Geometry 4.4 4.6 ongruence Proofs ecember 08, 2016 h 4 Review Problems pp.176 180 #7 36, 48,51,52 due MONY 12/12 h 5 Review Problems pp. 206 209 #15 50 h 6 Review Problems pp. 250 254 #9 19, 33 53 4.2
More information4-2 Triangle Congruence Conditions. Congruent Triangles - C F. and
4-2 Triangle ongruence onditions ongruent Triangles -,, ª is congruent to ª (ª ª) under a correspondence of parts if and only if 1) all three pairs of corresponding angles are congruent, and 2) all three
More informationMaintaining Mathematical Proficiency
Name ate hapter 5 Maintaining Mathematical Proficiency Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. 1. ( 3, 1 ) and ( 5,
More informationGeo Final Review 2014
Period: ate: Geo Final Review 2014 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. n angle measures 2 degrees more than 3 times its complement. Find the
More informationGeometry Honors. Midterm Review
eometry onors Midterm Review lass: ate: eometry onors Midterm Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1 What is the contrapositive of the statement
More informationWarm-Up. Find the domain and range:
Warm-Up Find the domain and range: Geometry Vocabulary & Notation Point Name: Use only the capital letter, without any symbol. Line Name: Use any two points on the line with a line symbol above. AB Line
More informationUnit 4 Day by Day. Day Sections and Objectives Homework. Monday October and 4.9 Packet Pages 1-3
Unit 4 ay by ay ay Sections and Objectives Homework Monday October 26 U41 4.2 and 4.9 Packet Pages 1-3 Types of triangles, isosceles and equilateral triangles Page 228 (23-31, 35-37) Page 288 (5-10, 17-20,
More informationGeometry Honors. Midterm Review
eometry Honors Midterm Review lass: ate: I: eometry Honors Midterm Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1 What is the contrapositive of the
More informationWhenever two figures have the same size and shape, they are called congruent. Triangles ABC and DEF are congruent. You can match up vertices like
Unit 1: orresponding Parts in a ongruence Section 1: ongruent Figures Whenever two figures have the same size and shape, they are called congruent. F D E Triangles and DEF are congruent. You can match
More informationGeometry Notes - Unit 4 Congruence
Geometry Notes - Unit 4 ongruence Triangle is a figure formed by three noncollinear points. lassification of Triangles by Sides Equilateral triangle is a triangle with three congruent sides. Isosceles
More informationThe side that is opposite the vertex angle is the base of the isosceles triangle.
Unit 5, Lesson 6. Proving Theorems about Triangles Isosceles triangles can be seen throughout our daily lives in structures, supports, architectural details, and even bicycle frames. Isosceles triangles
More informationSmart s Mill Middle School
Smart s Mill Middle School Geometry Semester Exam Review 0 03 You must show your work to receive credit! Mrs. nderson and Mrs. ox note to remember, for this review N the actual exam: It is always helpful
More informationGeometry Rules! Chapter 4 Notes. Notes #22: Section 4.1 (Congruent Triangles) and Section 4.5 (Isosceles Triangles)
Name: Geometry Rules! hapter 4 Notes - 1 - Period: Notes #: Section 4.1 (ongruent Triangles) and Section 4.5 (Isosceles Triangles) ongruent Figures orresponding Sides orresponding ngles Triangle ngle-sum
More informationThe SAS Postulate requires the same information as the LL Theorem, so it can be used to prove two right triangles congruent.
State whether each sentence is or false. If false, replace the underlined word or phrase to make a sentence. 1. The vertex angles of an isosceles triangle are false; The base angles of an isosceles triangle
More informationName Class Date. This shows that A corresponds to Q. Therefore, A Q. This shows that BC corresponds to RS. Therefore, BC RS.
ame lass ate Reteaching ongruent igures Given QRST, find corresponding parts using the names. Order matters. or example, QRST or example, QRST This shows that corresponds to Q. Therefore, Q. This shows
More informationThe SAS Postulate requires the same information as the LL Theorem, so it can be used to prove two right triangles congruent.
State whether each sentence is or false. If false, replace the underlined word or phrase to make a sentence. 1. The vertex angles of an isosceles triangle are false; The base angles of an isosceles triangle
More informationdescribes a ray whose endpoint is point A. TRUE g. A plane has no thickness. TRUE h. Symbols XY and YX describe the same line. TRUE i.
Geometry Ms. H. Ray, 010 NSWRS TO TH RVIW FOR TH GOMTRY MITRM XM. 1. True or False? e prepared to explain your answer. a. efinitions and theorems are very important in mathematics but every mathematical
More informationChapter 4. Section 4-1. Classification by Angle. Acute Triangle - a triangle with 3 acute angles!
hapter 4 ongruent Triangles That is water, not cement Section 4-1 lassifying Triangles lassification by ngle cute Triangle - a triangle with 3 acute angles! Equiangular Triangle - a triangle with 3 congruent
More information(Current Re nweb Grade)x.90 + ( finalexam grade) x.10 = semester grade
2//2 5:7 PM Name ate Period This is your semester exam which is worth 0% of your semester grade. You can determine grade what-ifs by using the equation below. (urrent Re nweb Grade)x.90 + ( finalexam grade)
More informationB. Algebraic Properties Reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division
. efinitions 1) cute angle ) cute triangle 3) djacent angles 4) lternate exterior angles 5) lternate interior angles 6) ltitude of a triangle 7) ngle ) ngle bisector of a triangle 9) ngles bisector 10)
More informationChapter 4 Triangles Overview
Chapter 4 Triangles Overview Ohio State Standards for Mathematics: G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding
More informationDO NOT LOSE THIS REVIEW! You will not be given another copy.
Geometry Fall Semester Review 2011 Name: O NOT LOS THIS RVIW! You will not be given another copy. The answers will be posted on your teacher s website and on the classroom walls. lso, review the vocabulary
More information1. What is the sum of the measures of the angles in a triangle? Write the proof (Hint: it involves creating a parallel line.)
riangle asics irst: Some basics you should already know. eometry 4.0 1. What is the sum of the measures of the angles in a triangle? Write the proof (Hint: it involves creating a parallel line.) 2. In
More informationReady to Go On? Skills Intervention 4-1 Classifying Triangles
4 Ready to Go On? Skills Intervention 4-1 lassifying Triangles Find these vocabulary words in Lesson 4-1 and the Multilingual Glossary. Vocabulary acute triangle equiangular triangle right triangle obtuse
More informationUnit 4 Congruent Triangles.notebook. Geometry. Congruent Triangles. AAS Congruence. Review of Triangle Congruence Proofs.
Geometry Congruent Triangles AAS Congruence Review of Triangle Congruence Proofs Return to Table 1 Side opposite Side Side the sides of triangles Adjacent Sides - two sides sharing a common vertex leg
More informationYou try: What is the definition of an angle bisector? You try: You try: is the bisector of ABC. BD is the bisector of ABC. = /4.MD.
US Geometry 1 What is the definition of a midpoint? midpoint of a line segment is the point that bisects the line segment. That is, M is the midpoint of if M M. 1 What is the definition of an angle bisector?
More informationGeometry/Trig 2 Unit 4 Review Packet page 1 Part 1 Polygons Review
Unit 4 Review Packet page 1 Part 1 Polygons Review ate: 1) nswer the following questions about a regular decagon. a) How many sides does the polygon have? 10 b) What is the sum of the measures of the interior
More informationGeometry Ch 7 Quadrilaterals January 06, 2016
Theorem 17: Equal corresponding angles mean that lines are parallel. Corollary 1: Equal alternate interior angles mean that lines are parallel. Corollary 2: Supplementary interior angles on the same side
More informationName: Unit 4 Congruency and Triangle Proofs
Name: Unit 4 ongruency and Triangle Proofs 1 2 Triangle ongruence and Rigid Transformations In the diagram at the right, a transformation has occurred on. escribe a transformation that created image from.
More informationProving Theorems about Lines and Angles
Proving Theorems about Lines and Angles Angle Vocabulary Complementary- two angles whose sum is 90 degrees. Supplementary- two angles whose sum is 180 degrees. Congruent angles- two or more angles with
More informationWhat is a(n); 2. acute angle 2. An angle less than 90 but greater than 0
Geometry Review Packet Semester Final Name Section.. Name all the ways you can name the following ray:., Section.2 What is a(n); 2. acute angle 2. n angle less than 90 but greater than 0 3. right angle
More information4-1. Classifying Triangles. Lesson 4-1. What You ll Learn. Active Vocabulary
4-1 Classifying Triangles What You ll Learn Scan Lesson 4-1. Predict two things that you expect to learn based on the headings and the Key Concept box. 1. Active Vocabulary 2. New Vocabulary Label the
More informationGeometry. Slide 1 / 183. Slide 2 / 183. Slide 3 / 183. Congruent Triangles. Table of Contents
Slide 1 / 183 Slide 2 / 183 Geometry ongruent Triangles 2015-10-23 www.njctl.org Table of ontents Slide 3 / 183 ongruent Triangles Proving ongruence SSS ongruence SS ongruence S ongruence S ongruence HL
More information3. (9x + 9) x 45 5x. 5. (7x + 6)
5 hapter eview 5.1 ngles of riangles (pp. 231 238) ynamic Solutions available at igideasath.com lassify the triangle by its sides and by measuring its angles. he triangle does not have any congruent sides,
More informationGeometry. Chapter 3. Congruent Triangles Ways of Proving Triangles Corresponding Parts of Δ s (CP Δ=) Theorems Based on Δ s
Geometry hapter 3 ongruent Triangles Ways of Proving Triangles orresponding Parts of Δ s (P Δ=) Theorems ased on Δ s Geometry hapter 3 ongruent Triangles Navigation: lick on sheet number to find that sheet.
More informationSlide 1 / 343 Slide 2 / 343
Slide 1 / 343 Slide 2 / 343 Geometry Quadrilaterals 2015-10-27 www.njctl.org Slide 3 / 343 Table of ontents Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Rhombi, Rectangles
More informationSemester Test Topic Review. Correct Version
Semester Test Topic Review Correct Version List of Questions Questions to answer: What does the perpendicular bisector theorem say? What is true about the slopes of parallel lines? What is true about the
More informationPOTENTIAL REASONS: Definition of Congruence:
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 informationCongruent triangle: all pairs of corresponding parts are congruent. Congruent Polygons: all pairs of corresponding parts are congruent.
Notes Page 1 3.1 Notes Wednesday, October 01, 2008 8:33 PM efinitions: 2. ongruent triangle: all pairs of corresponding parts are congruent. ongruent Polygons: all pairs of corresponding parts are congruent.
More informationReteach. Congruence and Transformations
Congruence and Transformations TYPES OF TRANSFORMATIONS (centered at (0, 0)) Translation (slide): (x, y) (x a, y b) Reflection y-axis: (x, y) ( x, y) x-axis: (x, y) (x, y) Rotation 90 clockwise: (x, y)
More informationUNIT 5 SIMILARITY AND CONGRUENCE
UNIT 5 SIMILARITY AND CONGRUENCE M2 Ch. 2, 3, 4, 6 and M1 Ch. 13 5.1 Parallel Lines Objective When parallel lines are cut by a transversal, I will be able to identify angle relationships, determine whether
More informationTheorems, Postulates, and Properties for Use in Proofs
CP1 Math 2 Name Unit 1: Deductive Geometry: Day 21-22 Unit 1 Test Review Students should be able to: Understand and use geometric vocabulary and geometric symbols (,,, etc) Write proofs using accurate
More informationGeometry EOC Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Geometry EO Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Show that the conjecture is false by finding a counterexample. If, then. a., c., b.,
More informationTheorem (NIB), The "The Adjacent Supplementary Angles" Theorem (Converse of Postulate 14) :
More on Neutral Geometry I (Including Section 3.3) ( "NI" means "NOT IN OOK" ) Theorem (NI), The "The djacent Supplementary ngles" Theorem (onverse of ostulate 14) : If two adjacent angles are supplementary,
More informationProving Lines Parallel
Proving Lines Parallel Proving Triangles ongruent 1 Proving Triangles ongruent We know that the opposite sides of a parallelogram are congruent. What about the converse? If we had a quadrilateral whose
More informationGeometry Level 1 Midterm Review Packet. I. Geometric Reasoning (Units 1 & 2) Circle the best answer.
2015 Midterm Outline (120pts) I. 28 Multiple Choice (28pts) II. 12 True & False (12pts) III. 13 Matching (13pts) IV. 14 Short Answer (49pts) V. 3 Proofs (18pts) VI. 10 Common Assessment (10pts) Geometry
More informationGeometry - Concepts 9-12 Congruent Triangles and Special Segments
Geometry - Concepts 9-12 Congruent Triangles and Special Segments Concept 9 Parallel Lines and Triangles (Section 3.5) ANGLE Classifications Acute: Obtuse: Right: SIDE Classifications Scalene: Isosceles:
More informationNov 9-12:30 PM. Math Practices. Triangles. Triangles Similar Triangles. Throughout this unit, the Standards for Mathematical Practice are used.
Triangles Triangles Similar Triangles Nov 9-12:30 PM Throughout this unit, the Standards for Mathematical Practice are used. MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly
More informationStop signs would be examples of congruent shapes. Since a stop sign has 8 sides, they would be congruent octagons.
hapter 5 ongruence Theorems -! s In math, the word congruent is used to describe objects that have the same size and shape. When you traced things when you were a little kid, you were using congruence.
More informationGeometry Honors Semester 1
Geometry Honors Semester 1 Final Exam Review 2017-2018 Name: ate: Period: Formulas: efinitions: 1. Slope - 1. omplementary 2. Midpoint - 2. Supplementary 3. isect 3. istance - 4. Vertical ngles 4. Pythagorean
More informationGeometry Review for Test 3 January 13, 2016
Homework #7 Due Thursday, 14 January Ch 7 Review, pp. 292 295 #1 53 Test #3 Thurs, 14 Jan Emphasis on Ch 7 except Midsegment Theorem, plus review Betweenness of Rays Theorem Whole is Greater than Part
More informationReteaching Exploring Angles of Polygons
Name Date lass Eploring Angles of Polygons INV X 3 You have learned to identify interior and eterior angles in polygons. Now you will determine angle measures in regular polygons. Interior Angles Sum of
More informationGeometry Level 1 Midterm Review Packet
Geometry L1 2017 Midterm Topic List Unit 1: Basics of Geometry 1. Point, Line, Plane 2. Segment Addition Postulate 3. Midpoint Formula, Distance Formula 4. Bisectors 5. Angle Pairs Unit 2: Logical Reasoning
More informationGeometry Rules! Chapter 4 Notes. Notes #20: Section 4.1 (Congruent Triangles) and Section 4.4 (Isosceles Triangles)
Geometry Rules! hapter 4 Notes Notes #20: Section 4.1 (ongruent Triangles) and Section 4.4 (Isosceles Triangles) ongruent Figures orresponding Sides orresponding ngles *** parts of triangles are *** Practice:
More informationCongruent Triangles. 1. In the accompanying diagram, B is the midpoint of
ongruent Triangles Name: ate: 1. In the accompanying diagram, is the midpoint of,, E, and = E. Which method of proof may be used to prove = E?. SS = SS. S = S. HL = HL. S = S 4. In the accompanying diagram
More informationNovember 21, Angles of Triangles
Geometry Essential Question How are the angle measures of a triangle related? Goals Day 1 Classify triangles by their sides Classify triangles by their angles Identify parts of triangles. Find angle measures
More informationdescribes a ray whose endpoint is point A. g. A plane has no thickness. h. Symbols XY and YX describe the same line. i. Symbols AB
RVIW FOR TH GOMTRY MITRM XM. 1. True or False? e prepared to explain your answer. a. efinitions and theorems are very important in mathematics but every mathematical system must contain some undefined
More informationCHAPTER 5 RELATIONSHIPS WITHIN TRIANGLES
HPTR 5 RLTIONSHIPS WITHIN TRINGLS In this chapter we address three ig IS: 1) Using properties of special segments in triangles ) Using triangle inequalities to determine what triangles are possible 3)
More information4 Triangles and Congruence
www.ck12.org CHAPTER 4 Triangles and Congruence Chapter Outline 4.1 TRIANGLE SUMS 4.2 CONGRUENT FIGURES 4.3 TRIANGLE CONGRUENCE USING SSS AND SAS 4.4 TRIANGLE CONGRUENCE USING ASA, AAS, AND HL 4.5 ISOSCELES
More informationPoints, Lines, and Planes 1.1
Points, Lines, and Planes 1.1 Point a location ex. write as: Line made up of points and has no thickness or width. ex. c write as:, line c ollinear points on the same line. Noncollinear points not on the
More informationGeometry Midterm Review 2019
Geometry Midterm Review 2019 Name To prepare for the midterm: Look over past work, including HW, Quizzes, tests, etc Do this packet Unit 0 Pre Requisite Skills I Can: Solve equations including equations
More informationVOCABULARY. Chapters 1, 2, 3, 4, 5, 9, and 8. WORD IMAGE DEFINITION An angle with measure between 0 and A triangle with three acute angles.
Acute VOCABULARY Chapters 1, 2, 3, 4, 5, 9, and 8 WORD IMAGE DEFINITION Acute angle An angle with measure between 0 and 90 56 60 70 50 A with three acute. Adjacent Alternate interior Altitude of a Angle
More informationProperties of Rhombuses, Rectangles, and Squares
6- Properties of Rhombuses, Rectangles, and Squares ontent Standards G.O. Prove theorems about parallelograms... rectangles are parallelograms with congruent diagonals. lso G.SRT.5 Objectives To define
More informationAn Approach to Geometry (stolen in part from Moise and Downs: Geometry)
An Approach to Geometry (stolen in part from Moise and Downs: Geometry) Undefined terms: point, line, plane The rules, axioms, theorems, etc. of elementary algebra are assumed as prior knowledge, and apply
More informationAB = x, BC = x + 10, AC = 3x + 2. Find x. 10. Draw an obtuse angle
Name: Geometry inal am Review. ind the net two numbers in each pattern a.,, 4, 40,,. =, = + 0, = + 0. raw an obtuse angle. M M is the midpoint of M = - M = b. -4,, -6,,,. 6. ind the midpoint of the segment
More informationAngles of Triangles. Essential Question How are the angle measures of a triangle related?
2. ngles of Triangles Essential Question How are the angle measures of a triangle related? Writing a onjecture ONSTRUTING VILE RGUMENTS To be proficient in math, you need to reason inductively about data
More informationTo use and apply properties of isosceles and equilateral triangles
- Isosceles and Equilateral riangles ontent Standards G.O. Prove theorems about triangles... base angles of isosceles triangles are congruent... lso G.O., G.SR. Objective o use and apply properties of
More informationSegment Addition Postulate: If B is BETWEEN A and C, then AB + BC = AC. If AB + BC = AC, then B is BETWEEN A and C.
Ruler Postulate: The points on a line can be matched one to one with the REAL numbers. The REAL number that corresponds to a point is the COORDINATE of the point. The DISTANCE between points A and B, written
More informationGeometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review
Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Polygon a closed plane figure with at least 3 sides that are segments -the sides do not intersect except at the vertices N-gon -
More informationGeometry. Chapter 4 Resource Masters
Geometry hapter 4 esource Masters NME E PEI 4 eading to Learn Mathematics Vocabulary uilder his is an alphabetical list of the key vocabulary terms you will learn in hapter 4. s you study the chapter,
More informationHonors Geometry Semester 1 Exam Review. Hour: CB and CA are opposite rays and CD and CA. Show all your work whenever possible.
Honors Geometry Semester 1 Exam Review Name: Hour: Show all your work whenever possible 1escribe what the notation RS stands for Illustrate with a sketch 8 Find the distance between the points (1, 4) and
More informationGeometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12)
Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12) Date: Mod: Use the figure at the right for #1-4 1. What is another name for plane P? A. plane AE B. plane A C. plane BAD D. plane
More informationSummer Dear Geometry Students and Parents:
Summer 2018 Dear Geometry Students and Parents: Welcome to Geometry! For the 2018-2019 school year, we would like to focus your attention to the prerequisite skills and concepts for Geometry. In order
More informationObjective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms
Unit 1 asics of Geometry Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms 1. Point has no dimension, geometrically looks
More informationVideos, Constructions, Definitions, Postulates, Theorems, and Properties
Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos Proof Overview: http://tinyurl.com/riehlproof Modules 9 and 10: http://tinyurl.com/riehlproof2 Module 9 Review: http://tinyurl.com/module9livelesson-recording
More informationTranslating Triangles in the Coordinate Plane
hapter Summar Ke Terms transformation congruent line segments (71) () image congruent (71) angles () translation corresponding (71) sides () rotation corresponding (73) angles () SSS ongruence Theorem
More informationChapter 4 Triangles: Congruency & Similarity
1 Chapter 4 Triangles: Congruency & Similarity Concepts & Skills Quilting is a great American pastime especially in the heartland of the United States. Quilts can be simple in nature or as in the photo
More informationAngle Unit Definition Packet
ngle Unit Definition Packet Name lock Date Term Definition Notes Sketch djacent ngles Two angles with a coon, a coon you normay name and, and no coon interior points. 3 4 3 and 4 Vertical ngles Two angles
More informationMath-2. Lesson 7-4 Properties of Parallelograms And Isosceles Triangles
Math-2 Lesson 7-4 Properties of Parallelograms nd Isosceles Triangles What sequence of angles would you link to prove m4 m9 3 1 4 2 13 14 16 15 lternate Interior Corresponding 8 5 7 6 9 10 12 11 What sequence
More informationLesson 1.9.1: Proving the Interior Angle Sum Theorem Warm-Up 1.9.1
NME: SIMILRITY, CONGRUENCE, ND PROOFS Lesson 9: Proving Theorems bout Triangles Lesson 1.9.1: Proving the Interior ngle Sum Theorem Warm-Up 1.9.1 When a beam of light is reflected from a flat surface,
More informationFALL SEMESTER EXAM Directions: You must show work for all the problems. Unit 1. Angle. Angle Addition Postulate. Angle Bisector. Length of a segment
Name FALL SEMESTER EXAM Directions: You must show work for all the problems. Unit 1 Period Angle Angle Addition Postulate Angle Bisector Length of a segment Line Midpoint Right Angle Segment Segment Addition
More informationa triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
More informationChapter 4 part 1. Congruent Triangles
Chapter 4 part 1 Congruent Triangles 4.1 Apply Triangle Sum Properties Objective: Classify triangles and find measures of their angles. Essential Question: How can you find the measure of the third angle
More informationALGEBRA For each triangle, find x and the measure of each side. 1. LMN is an isosceles triangle, with LM = LN, LM = 3x 2, LN = 2x + 1, and MN = 5x 2.
Find each measure ALGEBRA For each triangle, find x and the measure of each side 4 1 LMN is an isosceles triangle, with LM = LN, LM = 3x 2, LN = 2x + 1, and MN = 5x 2 a x = 1; LM = 1, LN = 3, MN = 4 b
More informationFGCU Invitational Geometry Individual 2014
All numbers are assumed to be real. Diagrams are not drawn to scale. For all questions, NOTA represents none of the above answers is correct. For problems 1 and 2, refer to the figure in which AC BC and
More informationB M. and Quad Quad MNOP
hapter 7 ongruence Postulates &Theorems -Δ s In math, the word congruent is used to describe objects that have the same size and shape. When you traced things when you were a little kid, you were using
More informationGeometry Chapter 5 Review Sheet
Geometry hapter 5 Review Sheet Name: 1. List the 6 properties of the parallelogram. 2. List the 5 ways to prove that a quadrilateral is a parallelogram. 3. Name two properties of the rectangle that are
More information$100 $200 $300 $400 $500
Round 2 Final Jeopardy The Basics Get that Angle I Can Transform Ya Triangle Twins Polygon Party Prove It! Grab Bag $100 $100 $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $200 $200 $300 $300 $300
More informationGEOMETRY is the study of points in space
CHAPTER 5 Logic and Geometry SECTION 5-1 Elements of Geometry GEOMETRY is the study of points in space POINT indicates a specific location and is represented by a dot and a letter R S T LINE is a set of
More informationChapter 1-2 Points, Lines, and Planes
Chapter 1-2 Points, Lines, and Planes Undefined Terms: A point has no size but is often represented by a dot and usually named by a capital letter.. A A line extends in two directions without ending. Lines
More informationGeometry Quarter 4 Test Study Guide
Geometry Quarter 4 Test Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,
More informationGeometry Review. Description. Question #1. Question #2. Question #3. ΔDEC by ASA? 5/17/2017 Synergy TeacherVUE. Geometry CSA Review
escription Geometry S Review Geometry Review Question #1 If Δ and ΔXYZ are congruent, which of the following statements below is not true? ngle and angle Y are congruent. ngle and angle ZXY are congruent.
More informationGeometry Third Quarter Study Guide
Geometry Third Quarter Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,
More informationGeometry. Quadrilaterals. Slide 1 / 189. Slide 2 / 189. Slide 3 / 189. Table of Contents. New Jersey Center for Teaching and Learning
New Jersey enter for Teaching and Learning Slide 1 / 189 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
More informationBasics of Geometry Unit 1 - Notes. Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes.
asics of Geometry Unit 1 - Notes Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms 1. Point has no dimension, geometrically
More informationGeometry Definitions, Postulates, and Theorems
Geometry efinitions, Postulates, and Theorems hapter : Similarity Section.1: Ratios, Proportions, and the Geometric ean Standards: Prepare for 8.0 Students know, derive, and solve problems involving the
More information