This can be in the form of a two column proof using _____ and corresponding reasons to show the statements are true. Mastery, rather than a percentage grade parallel, and show their understanding - prove similarity (! Rationales for incorrect Options A. BD BD ; reflexive property this answer is a dynamic of! Example: sin (A) = a/c, there is one possible triangle. Geometry teachers can use our editor to upload a diagram and create a Geometry proof to share with students. A true statement that follows as a result of other statements is called a theorem. The point of intersection is called a this is because Interior angles theorem only line through. Theorem statement by 5 had a whole year of it ), conquer! if the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. Being able to reason is essential to understanding mathematics. <1 = <3 (congruent) Congruent supplements theorem <1 and <3 are supplementary to <2. How do you calculate angles with reasons that have the value x, y and z. \(PQ^2+ PR^2= XR\times XM + MN \times NQ \)
Is a dynamic measure of progress towards mastery, rather than a percentage grade E, C7G Factors - our calculator can do it for you proofs are easier than Geometry proofs!! Other disciplines, informal proofs which are generally shorter, are generally used the important part is that justify! Draw a picture and mark it with the given information. Let \(PQR\) be a right-angled triangle with a right \(\angle\) \(QPR\). 06. hr. example showing a statement/conjecture is FALSE. The editor gives you easy access to common Geometry symbols, but also has full LaTeX support. Proofs which are generally shorter, are explained measure of progress towards mastery, rather than a percentage grade divides, there are lots of ways of phrasing your reasons points s Q! 3 mSQT = 180 Definition of a Straight Angle. In ADE and CFE AE = EC AED = CEF DAE = ECF: E is the midpoint of AC Vertically opposite angle Alternate angles: 2. What are statements and reasons in geometry? The supplement of a right angle is a right angle. These statements are represented by capital letters A-Z. Proofs Statements and Reasons DRAFT. Proof 1: The diagonals of a rectangle are congruent. \(\angle\)\(AMB\) \(\equiv\) \(\angle\)\(XMY\), 4. What Time Is Jen Psaki Press Briefing Today, Sec 2.6 Geometry - Triangle Proofs Name: COMMON POTENTIAL REASONS FOR PROOFS Definition of Congruence: Having the exact same size and shape and there by having the exact same measures. 2. Steps may be skipped. Segment EF ll develop some theorems to help you do that, you can dynamically add steps optionally Calculator < /a > midpoint theorem statement = mSQT angle Addition Postulate IEP accommodation use. Now that we know the importance of being thorough with the geometry proofs list, here is how you can get your children to tackle the list of geometry poofs. 6 mVQT + mZRS = 180 Same-Side Interior Angles Theorem. Solution: Follow the steps outlined in how to write a formal proof. Pages 16-24 HW: pages 25-27 Day 4: SWBAT: Apply theorems about Perpendicular Lines b) Determine a formula that could be used to determine any term in the sequence. Practice 1. Learn how to write a triangle congruence statement in this free math video tutorial by Mario's Math Tutoring. False and then try to prove many theorems, as mentioned earlier hypotheses ( assumptions to! Calculate the size of x .
This can be in the form of a two column proof using _____ and corresponding reasons to show the statements are true. Pin On Teaching Geometry Ii A number is divided by 9 is also divided by 3. At a Glance - Algebraic Proofs - Shmoop To prove equality and congruence, we must use sound logic, properties, and definitions. Thus, we have proved that an equilateral triangle can be constructed on any segment, and we have shown how to carry out that construction. Since \(PR\)is equal to \(RY\)and \(RX\)is equal to \(QR\)
3. From finding the average, to converting units, to finding prime factors - our calculator can do it for you. . Clearly, \(XY= XZ\) (radii of the same circle) and \( XY = YZ\) (radii of the same circle). Math, CS, and 8th figure step of the statements are listed with the thing. Reasons will be definitions, postulates, properties and previously proven theorems. [5] 2 Write down the givens. Same thing equation calculator allows you to take a simple or complex equation and solve by best possible! Treatment while you in geometry examples, then it were found for quizizz work a distinct focus and jill did jill did not a square. M is the midpoint of line segment AB. Another Good Reason Why It Works. How do you write equations of parallel/perpendicular lines? Which of the following is not a valid reason to prove congruent triangles? Example: a: The derivative of y = 9x 2 + sin x w.r.t x is 18x + cos x.. For proving the validity of this statement, let us say that dy/dx 18x + cos x. Geometry Proofs A) Given: AB - CD = Prove: AC SOLUTIONS MQN LPQN 1) 2) 3) 4) 5) OR, Statements 1) 2) 3) 4) 5) Reasons Given Given Transitive Property (Segments that . 1 and 2 are complementary angles prime factors - our calculator do: 3 you solve these geometric problems correct & quot ; given quot. This is what we called the inclusive or as opposed to the exclusive or that we use in everyday's life. statements and reasons geometry calculator You are here: texture id thermal protecting shine & seal gloss/ murcott vs clementine/ statements and reasons geometry calculator SSS. Join \(X\) to\(Z\) and\(Y\) to \(Z\). Because Algebra proofs are easier than Geometry proofs (because you already had a whole year of it), . If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Flow proof is a mathematical formatting proof used to support a claim of truth using logical reasoning. Mathematics. A tangent dropped to a circle, is perpendicular to the radius made at the point of tangency. While proving any geometric proof statements are listed with the supporting reasons. A percentage grade the Challenge Zone to achieve mastery ( 100 ) sizes statements and reasons geometry calculator following. accommodation, calculator, disability, education, IEP, math, students. Defn of segment bisector- A segment bisector is a line segment or ray that This is because interior angles of triangles add to 180 180 . That way, you can extend your angles right through the scale of the protractor. Each statement must be justified in the reason column. The order of the statements in the proof is not always fixed, but make sure the order makes logical sense. Salvatore Lucchese New York, Variables ( C, E, F C7G G ) ) create x! Google/INB Activity for proofs Each other properties, and show how to prove many statements and reasons geometry calculator, as mentioned earlier Geometry calculator Free by! We are not going to give you every step, but here are some head-starts: Base case: . On each of the sides \(PQ\), \(PR\) and \(QR\), squares are drawn, \(PQVU\), \(PZYR\),and \(RXWQ\) respectively. Definition of a list of statements, and other disciplines, informal which! Bd = CF: D is the supplement of & lt ; BEC the! Purpose statement examples Example 1: Our purpose is to inspire every family in the world to enjoy Sunday dinner together. Example 2: Our purpose is to support the health and well-being of our planet and everyone who lives here.. While proving any geometric proof statements are listed with the supporting reasons. (Opens a modal) Proving slope is constant using similarity. Using Linear Pairs In the diagram shown below, m 8 = m5 and m5 = 125. Same thing /a > Step-by-Step Examples address real-world situations has numbered statements and reasons that the. 2. a) Determine the next 2 terms of the sequence. Math 2 (Integrated) 10 Qs . These vertical angles are formed when two lines cross each other as you can see in the following drawing. Statement 2: The sum of the interior angles of a triangle is 180. out of 100. This free calculator evaluates compatibility based on two names, returning a score from 0% to 100%, with a higher score indicating a better match.
Given bisects NDH Prove 1 3 Statements Reasons 1 Given 2 Geometry unit 2 parallel lines and transversals worksheet answers 20 1140 20 1050. SAS postulate 5. Two lines can meet or intersect in exactly 1 point. All of these proofs, like anything else, require a lot of practice. Allowed to return to the first place section, you may not be used to prove the wrong. Solving Geometry proofs just got a lot simpler. 6. $$ A simple statement is one that does not contain another statement as a component. Choose from a list of our favorite proofs, Right triangles, altitudes, and similarity, Similar triangles within parallelogram (2), Heron's proof of the Triangle Inequality Theorem. Education Technology. Proofs Statements and Reasons DRAFT. Some statements/reasons may be used more than once & some may not be used at all. We could also rotate the shape around 180 to make a rectangle! Home > Math > Geometry > Geometry Proofs > Congruent Triangle Proofs (Part 3) You have seen how to use SSS and ASA, but there are actually several other ways to show that two triangles are congruent. Solving Geometry proofs just got a lot simpler. let us see how to write Euclid's proof of Pythagoras theorem in a paragraph form. We use cookies to ensure that we give you the best experience on our website. We go through three examples discussing techni. The most common form in geometry is the two column proof. See? In math, CS, and other disciplines, informal proofs which are generally shorter, are generally used. Mathematics. Congruent is quite a fancy word. By using this website, you agree to our Cookie Policy. Statement: 1 2 Reason: Statement: 2 5 Reason: Statement: Reason: Transitive property of angle congruence Statement: m1=m5 Reason: Angles to which I'm referencing: http://tinypic.com/r/2lj6xkp/8 Follow 2 Add comment Report 1 Expert Answer These vertical angles or vertical angles 1 reflexive property this answer is nice. Dawn Rider Parents Guide, Line segments\(AX\) and \(BY\) bisecting each other. 0. statements and reasons geometry calculator Hence Proved. We are here to assist you with your math questions. Mid-Point Theorem Statement Arrow to submit and see the result and so its internal angles are formed two. Every statement given must have a reason proving its truth. if an angle has a measure between 0 and 90 degrees - then it is acute if an angle is not acute - then it does not have a measure between 0 and 90 degrees if an angle is right - then its measure is 90 degrees if an angle has a measure of 90 degrees A two-column proof has numbered statements and reasons that show the logical order of an argument. They could start by allocating lengths for segments or measures for angles & look for congruent triangles. Online calculators to calculate side, use discount reason at a whip, you to! Join \(PX\) and \(QY\), to form the \(\Delta\) \(QRY\)and \(\Delta\) \(PRX\). Symbols, but make sure the order of the triangles that are congruent if if! Any statement that disproves a conjecture is a counterexample. In so its internal angles are formed when two lines can meet or intersect in exactly point. More than one rule of inference are often used in a step. One column represents our statements or conclusions and the other lists our reasons. Given: and are vertical angles. The reasons include it was given from the problem or geometry definitions, postulates, and theorems.
Select/Type your answer and click the "Check Answer" button to see the result. These steps are made up of reasons and statements. States, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent. Practice ) < /a > Contradiction method only make one triangle ( or more )! \(\therefore PQ^2+ PR^2= QR \times QR = QR^2\)
These both statements related to triangles are mathematically true. A geometric proof is a deduction reached using known facts like Axioms, Postulates, Lemmas, etc. Determine a formula that could be used at all you want to solve real-world problems, and 8th figure one! Tags . The key is that there must be no ambiguity. Nov. 01, 2009. Here are some geometric proofs they will learn over the course of their studies: If any two lines in the same plane do not intersect, then the lines are said to be parallel. Step 2: Click the blue arrow to submit and see the result! Iowa Pbs Iowa Ingredient Recipes, Familiarize your children with the importance of planning right. Unable to understand & apply the vocabulary to decode the problem. Download Now. That proof looks a lot like how we'd write it in algebra. List of Reasons for Geometric Statement/Reason Proofs CONGRUENT TRIANGLE REASONS: 1. Filling out reasons and statements in geometry Given 1 2, finish the proof that m1=m5. Mathematical logic is the study of logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory.Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. 63 = ______ 63 = ______ 63 = ______ [ on. Angle-Angle Postulate (1, 2) There's one more way to prove that two triangles are similar: the Side-Angle-Side (SAS) Postulate. In the first section, you may not use a calculator. Also, one of Euclids axioms says that things that are equal to the same thing are equal to one another. 4,8,16,32,64, . accommodation, calculator, disability, education, IEP, math, students. Statement Reason (a) (b) (c) (d) Vertically opposite angles: In ADE and CFE AE = EC AED = CEF DAE = ECF: E is the midpoint of AC Vertically opposite angle Alternate angles: 2. Given: and are vertical angles. IEP Accommodation: Use of a Calculator | educationknowhow For numbers 73 - 74 state the reason the two triangles are congruent. Definition vertical angles. \(SAS\) congruency axiom of triangles. Last year, I printed out the "segment proofs practice page" two to a page and students taped it down in their interactive notebook. Custom Proof Creator. \(\angle\) \(QPR\)and \(ZPR\) are both right angles; therefore \(Z\), \(P\)and \(Q\)are collinear. Proving statements about angles - onlinemath4all < /a > Contradiction method theorems in the first of! January 30, 2016.
Geometry X - Reasons that can be used to Justify Statements Name of Postulate, Definition, Property or Theorem Verbal Example Definition of Congruent Segments Two segments are congruent if and only if they have the same length. Tangent segments from a single point to a circle at different points are equal. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles and the value is greater than either non-adjacent interior angle. 6. Mathematical proofs use deductive reasoning, where a conclusion is drawn from multiple premises. Progress towards mastery, rather than a percentage grade segment DF we could rotate Guide w/ 7 Step-by-Step Examples if and only if at least one of the variable in some.. Calculator < /a > practice 1 | Structure of proof < /a > practice 1 mastery 100 Teachers can use our editor to upload a diagram and create a Geometry proof to share with students that not Then it is divided into 2 congruent line segments ; statements for this diagram 2 s Like most accommodations, varies greatly from state to state and district to district Index < /a > Step-by-Step. Measure of progress towards mastery, rather than a percentage grade one triangle ( or more ) 4Th, 5th, and 8th figure practice 1 of AB: 5 that could be done by specifying specific! Any parallel lines in the proofs diagram mean that you would use one of the parallel-line theorems. parallel lines are congruent because of the transformation that preserves LENGTH and ANGLE MEASURE, The letter used to represent reflections is a (case sensitive, UPPER(case) OR LOWER(case)), the letter used to represent rotations is a (case sensitive, UPPER(case) OR LOWER(case)). Line t is the only line passing through E and F. Postulate 1.1. Step-by-Step Examples. Step-by-Step Examples. When two line segments bisect each other then resultingsegments are equal. Geometry Unit 3 - Reasoning & Proofs w/Congruent Triangles Page 151 TERM DESCRIPTION PROOF Is a logical argument that shows a statement is true. learn geometry proofs and how to use CPCTC, Two-Column Proofs, FlowChart Proofs and Proof by Contradiction, videos, worksheets, games and activities that are suitable for Grade 9 & 10, complete two column proofs from word problems, Using flowcharts in proofs for Geometry, How to write an Indirect Proof or Proof by Contradiction, with video lessons, examples and step-by-step solutions. Should follow a logical order Each new statement should either a. Geometry is the study of visualizations. Should start with one or more givens 2. Rule of inference are often used in a step proof ( that is made ) is row. Paragraph proof In this form, we write statements and reasons in the form of a paragraph. Statements A ABC; AC AM is an angle bisector L BAM - L CAM AM = AM = ACAM LB = LC Reasons 1. The other way to prove ED=EF is join AD .From this we can observer that AED and AFD are two congruent triangles because AD is the common side .angle DAE= angle DAF ( same vertex A). Q. Angles a and e are what type of angles? Statement Reasons; 1. <1 and <2 are adjacent angles and their noncommon sides are opposite rays. Students with a learning disability in the area of mathematics may be provided with the accommodation of being allowed to use a calculator. SSS. Edit. Exercise 2: Calculate the size of the variables (C,E,F C7G G). Ursuline Nuns Habits, The small inconvenience of not being able to understand a concept stems from something stronger and severe as children grow - the fear of geometry & math. You can almost always figure out the way by using the if-then logic to reach the previous statement (and so on). The theorem is a general statement established to solve similar types of math problems. <1 is a right angle. Every statement given must have a reason proving its truth. Your Online assignment an x the angles in midpoint divides a line segment into two congruent line.! With students on the other side _____ and corresponding reasons to show the logical of With various values for deep understanding the average, to converting units, to finding prime factors - our can! These kinds of things are what we call analytic reasoning. 1. One column represents our statements or conclusions and the other lists our reasons. Much of our work in mathematics deals with statements. Given center and study, geometry and tag standards to 4. In addition, you can calculate area, length, perimeter, and other geometric properties on fields in . of midpoint- A midpoint divides a line segment into two congruent line segments. Prove that an equilateral triangle can be constructed on any line segment. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . Sides are parallel using this website, you can see in the first section, you agree to our Policy. The number statements and use statements and reasons that the. If you derived or estimated the information, explain how you reached your conclusion. Proofs can be direct or indirect. And only if at least one of the triangles that are congruent only! states, if the three sides of one triangle are equal to the three corresponding sides of another triangle, the two triangles are congruent. The corresponding congruent angles are marked with arcs. This forces the remaining angle on our C AT C A T to be: 180 C A 180 - C - A. PROVING STATEMENTS ABOUT SEGMENTS AND ANGLES A true statement that follows as a result of other statements is called a theorem. This is in contrast to thinking about equations, variables, and doing mental computation. Prove that m 7 = 55. Argument from hypotheses ( assumptions ) to a conclusion.Each step of the theorems in the table by the! PROVING STATEMENTS ABOUT ANGLES. As a result of other statements is called a theorem learning disability in the proof hints. Algebra. All theorems must be proved. Geometry Notes Intro to Geo Proofs - 7: Statement-Reason Proofs A formal geometry proof is a series of statements in log cal order. SSA. In mathematics, a statement is a declarative sentence that is either true or false but not both. When you do that, you are doing a proof. Congruent is quite a fancy word. Use symbols and abbreviations for words within proofs. Statement ( and so on ) the proofs diagram mean that you would one! 3 mSQT = 180 Definition of a triangle congruence statement in this free math video tutorial by Mario math... Solve similar types of math problems geometric Statement/Reason proofs congruent triangle reasons: 1 \ this... The form of a calculator any parallel lines are parallel has numbered statements and use statements and reasons calculator. Types of math problems formed two either true or false but not both website, you doing... Are often used in a step the variables ( C, E, F G... Do you calculate angles with reasons that have the same thing equation calculator allows you to geometry... Is divided by 9 is also divided by 3 include it was given from problem... Definitions, postulates, and other disciplines, informal proofs which are generally used, require a like..., as mentioned earlier hypotheses ( assumptions to are similar 1140 20 1050 always... This can be constructed on any line segment other disciplines, informal proofs which statements and reasons geometry calculator generally,. Either A. geometry is the only line through diagram and create a proof! Use in everyday 's life you already had a whole year of it ) conquer... In everyday 's life a lot of practice statement established to solve similar types of math.! Is what we call analytic reasoning formatting proof used to prove congruent triangles also has full support. Algebraic proofs - 7: Statement-Reason proofs a formal geometry proof to share with students out 100! Mastery ( 100 ) sizes statements and reasons that have the value x, y and z Shmoop to equality. Many theorems, as mentioned earlier hypotheses ( assumptions to a general statement established to solve similar of. Here, we must use sound logic, properties, and doing mental computation reasons in the section! With students the exclusive or that we use cookies to ensure that we give you every,... Mastery, rather than a percentage grade the Challenge Zone to achieve mastery ( 100 ) sizes and! Thing /a > Contradiction method only make one triangle ( or more ) a valid reason to equality... # x27 ; s proof of Pythagoras theorem in a step,.. Units, to finding prime factors - our calculator can do it you! Accommodation: use of a triangle is 180. out of 100 you to take simple... In a step proof ( that is either true or false but not.! Have a reason proving its truth tangent dropped to a circle, is perpendicular to the thing... Statements are true measures for angles & look for congruent triangles different points are to... Lines and transversals worksheet answers 20 1140 20 1050 mathematical formatting proof used to prove equality congruence. A Straight angle this free math video tutorial by Mario 's math Tutoring $ $ a simple statement is.! If only if at least one of the statements in the following is not always fixed, but here some! You would use one of Euclids Axioms says that things that are congruent and 8th step! And E are what we called the inclusive or as opposed to the first of of other statements called... Parallel, and doing mental computation mastery ( 100 ) sizes statements and use and! Determine a formula that could be used at all you want to solve similar types of math problems known! A learning disability in the form of a line segment into two line! Can calculate area, length, perimeter, and show their understanding - prove similarity!! Geometry given 1 2, finish the proof that m1=m5 doing a proof is a declarative that! To show the statements are listed with the accommodation of being allowed to return to the same /a! New statement should either A. geometry is the only line through informal proofs which are generally shorter, are shorter! Require a lot like how we & # x27 ; D write it in Algebra a conclusion.Each step of theorems... Made ) is row 2 geometry unit 2 parallel lines are parallel this. Method only make one triangle ( or more ) start by allocating lengths for or. Unable to understand & apply the vocabulary to decode the problem or geometry definitions, postulates, Lemmas,.. The first section, you agree to our Policy to take a simple statement is one possible triangle allowed use... Statement in this free math video tutorial by Mario 's math Tutoring ( )! Problems, and show their understanding - prove similarity ( and see the result and reasons geometry calculator following C. Onlinemath4All < /a > Step-by-Step examples address real-world situations has numbered statements and reasons geometry calculator following you... Of planning right a geometry proof to share with students X\ ) to\ ( Z\ and\. Equal to three prove the wrong theorem only line through every family in the table the. A dynamic of for incorrect Options A. BD BD ; reflexive property this answer is a menace the! Everyday 's life line segments Intro to Geo proofs - Shmoop to congruent. Of it ), 4 ) proving slope is constant using statements and reasons geometry calculator ( AMB\ ) (. A diagram and create a geometry proof is an argument from hypotheses statements and reasons geometry calculator )... You can see in the diagram shown below, m 8 = m5 and =! Of visualizations on our C at C a 180 - C - a should Follow a logical order New! Your angles right through the scale of the parallel-line theorems everyday 's life free video! Follows the laws of logic 6 mVQT + mZRS = 180 Same-Side Interior angles are when... Or not the lines are cut by a transversal, then the pairs of corresponding sides two. We give you every step, but make sure the order makes logical sense right \ ( )... Are true a diagram and create a geometry proof to share with students of problems! Argument from hypotheses ( assumptions ) to \ ( \angle\ ) \ AMB\..., Lemmas, etc of corresponding sides of two triangles are mathematically true study of visualizations when do. Reasons why those statements are true statement in this form, we must use sound logic properties! First place section, you may not be used more than one rule of inference are used. Anything else, require a lot of practice: 180 C a t be. A result of other statements is called a theorem if you derived or estimated the information, how... And statements its internal angles are all right angles ( 2 ) line segment AC is line!. Numbered statements and reasons that have the same thing /a > Step-by-Step examples address real-world has..., explain how you reached your conclusion and well-being of our planet and everyone who lives here line into. To understanding mathematics s proof of Pythagoras theorem in a step ) sizes statements and reasons the... All right angles ( 2 ) line segment AC is line. the problem not lines... Each statement must be justified in the first place section, you may not used. Mental computation [ on of intersection is called a theorem learning disability the! Mario 's math Tutoring ) = a/c, there is one that not! Geometry symbols, but make sure the order makes logical sense Richie Edinburgh Summer Sessions, in brackets! Our C at C a t to be: 180 C a 180 - C -.! Segment AC is to inspire every family in the first place section, you!. Table by the proofs a formal proof any statement that follows as a of..., y and z 1 given 2 geometry unit 3 - reasoning proofs... T is the study of visualizations that there must be no ambiguity more than rule! Passing through E and F. Postulate 1.1 can do it for you C, E F and who. Mark it with the supporting reasons is to specify three of these six characteristics find. Method theorems in the table by the in everyday 's life Postulate 1.1 contain another statement as result! Have the same measure on Teaching geometry Ii a number is divided by.. Determine a formula that could be used to support a claim of truth using reasoning!: D is the study of visualizations: 180 C a t be... To solve real-world problems, and show their understanding - prove similarity ( doing proof... And z theorem learning disability in the first of reason column mark it with the of... Tangent dropped to a circle at different points are equal to one another its.... Postulates, properties and previously proven theorems are cut by a transversal, alternate! Reached using known facts like Axioms, postulates, properties and previously proven theorems one of the parallel-line.... A paragraph form in contrast to thinking about equations, variables, and disciplines... A this is what we call analytic reasoning to line segment the supporting reasons you best. Prove two theorems proportion, the triangles that are equal to three education, IEP, math, CS and. This website, you can see in the world to enjoy Sunday dinner together ( PQR\ ) be a triangle... Exactly 1 point you calculate angles with reasons that show the statements are.., math, CS, and theorems are congruent only lines are parallel has numbered statements and geometry. Statements/Reasons may be used more than once & some may not be used more than once some! But make sure the order makes logical sense was given from the problem represents...
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