Triangle R: Horizontal side a is 2 units. How does the length of the hypotenuse in a right triangle compare to the lengths of the legs? The special properties of both of these special right triangles are a result of the. Next, show the same image but with three squares drawn in, each using one of the sides of the triangle as a side length. Now that you have read the material and watched the video, it is your turn to put in practice what you have learned. The triangle has a height of 3 units.

. We own the copyright in all the materials we create, and we license certain copyrights in software we use to run our site, manage credentials and create our materials; some of this copyrighted software may be embedded in the materials you download. order now. hXkkF+K%v-iS#p`kK{$xqu9p8a;&TKbChXhJv-?V`" Congruent figures. Define and calculate the cosine of angles in right triangles. Review right triangle trigonometry and how to use it to solve problems. CCSS.MATH.PRACTICE.MP3 Direct link to Aditya Lagoo's post What is the value of sine, Posted 3 years ago. The length of the hypotenuse of the triangle is square root of two times k units. / When you use this site, you are agreeing to comply with these Terms & Conditions and our Single User License Agreement. Fall 2022, GEOMETRY 101 Using Right Triangles to Evaluate Trigonometric Functions. Make sense of problems and persevere in solving them. The height of the triangle is 1. 11. Use special triangles to determine geometrically the values of sine, cosine, tangent for /3, /4 and /6, and use the unit circle to express the values of sine, cosine, and tangent for -x, +x, and 2-x in terms of their values for x, where x is any real number. Would the answer to this problem be 36 (square root of 3 times the square root of 3 to get 3, 2 times 6 to get 12, and 12 times 3 to get 36)? Arrange students in groups of 24. If the triangle is a right triangle, then \(a\) and \(b\) are used to represent the lengths of the legs, and \(c\) is used to represent the length of the hypotenuse (since the hypotenuse is always the longest side of a right triangle). (from Coburn and Herdlick's Trigonometry book) Solve a right triangle given one angle and one side. If the four shaded triangles in the figure are congruent right triangles, does the inner quadrilateral have to be a square? im so used to doing a2+b2=c 2 what has changed I do not understand. Our goal is to make the OpenLab accessible for all users. Complete the tables for these three triangles: Description:

Three triangles on a square grid labeled D, E, and F with sides a, b, and c. The triangles have the following measurements: Triangle D: Horizontal side a is 2 units. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. 4. It can be also used as a review of the lesson. He explains that, two straight lengths of wire are placed on the ground, forming vertical angles. We use cookies to offer you a better browsing experience, analyze site traffic, and personalize content. Triangle E: Horizontal side a is 2 units. N.RN.A.2 Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Please do not copy or share the Answer Keys or other membership content. All these questions will give you an idea as to whether or not you have mastered the material. The ratios come straight from the Pythagorean theorem. More than just an application; Interior Angles Of Triangles Homework 3 Answer Key. The Pythagorean Theorem. What is the difference between congruent triangles and similar triangles? Purpose of each question: spiral, foundational, mastery, developing, Strategies and representations used in daily lessons, Relationship to Essential Understandings of unit, Notice the progression of concepts through the unit using Unit at a Glance.. What was the relationship we saw for the right triangles we looked at? (The sum of the squares of the legs was equal to the square of the hypotenuse. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve applications involving angles of rotation. OUR's 68 Math Curriculum is available at https://openupresources.org/math-curriculum/. No, but it is approximately a special triangle. This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Explain a proof of the Pythagorean Theorem and its converse. sharwood's butter chicken slow cooker larry murphy bally sports detroit lesson 1: the right triangle connection answer key. What is the value of sine, cosine, and tangent? Each side of the sign is about 1.2 m long. how do i know to use sine cosine or tangent? Consider a 30-60-90 triangle with the longer leg measuring 9 inches. Third Angles Theorem. Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Students define angle and side-length relationships in right triangles. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. By using the Pythagorean Theorem, we obtain that. For special triangles some skills you need to master are: Angles, Square roots, and most importantly. Triangle B,sides= 2, 5, square root 33. The Pythagorean Theorem describes the relationship between the side lengths of right triangles. Model with mathematics. - Unit 8 right triangles and trigonometry homework 1 Get the answers you need, now!. I do not know how you can tell the difference on a protractor between 30 and 30.1 degrees. Direct link to Jack Huber's post With 45-45-90 and 30-60-9, Posted 6 years ago. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (). Dont skip them! Duis kalam stefen kajas in the enter leo. 72.0 u2 4. Direct link to Aryan's post What is the difference be, Posted 6 years ago. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. G.SRT.D.11 If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent. Remember: the Show Answer tab is there for you to check your work! Problem 1.1 BC= B C = Round your answer to the nearest hundredth. Triangle D, right, legs = 3,4. hypotenuse = 5. Then apply the formula of sin, you can find hypotenuse. Your friend claims that two isosceles triangles triangle ABC and triangle DEF . Boy, I hope you're still around. Lesson 1 3. Direct link to 91097027's post do i have to be specific, Posted 4 years ago. Side c slants downward and to the right. Prove theorems about triangles. So you need to pick the two answers that would get you to zero radians, plus positive and minus every other pi. F.TF.A.4 Use a calculator. (b) Based on your answer in (a), find , and in exact form. This triangle is special, because the sides are in a special proportion. Use similarity criteria to generalize the definition of sine to all angles of the same measure. If you are not 100% satisfied, we will refund you the purchase price you paid within 30 days. 8.EE.B.6 Maybe the answer wouldn't differ that much but it might make it a little more challenging to figure out. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. CCSS.MATH.PRACTICE.MP1 if you know the 60-degree side of a 30-60-90 triangle the 30-degree side is root 3 times smaller and the hypotenuse is 2/root 3 times longer. In this task, students can use squares or count grid units to find side lengths and check whether the Pythagorean identity \(a^2+b^2 = c^2\) holds or not. Rewrite expressions involving radicals and rational exponents using the properties of exponents. DISPUTES. Direct link to Rick's post The answer to your proble, Posted 3 years ago. Compare any outliers to the values predicted by the model. Students gain practice with determining an appropriate strategy for solving right triangles. Click on the indicated lesson for a quick catchup. Direct link to Francesco Blz's post In a triangle 30-60-90, i, Posted 5 years ago. but is not meant to be shared. Solve a right triangle given one angle and one side. Yes, but special right triangles have constant ratios, so if you learn how to do this, you can get answers faster. Annotate the target tasks for: Trigonometry connects the two features of a triangleangle measures and side lengthsand provides a set of functions (sine, cosine, tangent), reciprocals, and inverses of those functions to solve triangles given angle measures and side lengths. Diagonal side c slants downward and to the right and the triangle has a height of 1 unit. 8.G.B.8 Verify experimentally the properties of rotations, reflections, and translations: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Special Right Triangles Worksheet Answer Key.pdf - Google Drive . Spanish translation of the "B" assessments are copyright 2020 byIllustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Construct viable arguments and critique the reasoning of others. In Topic B, Right Triangle Trigonometry, and Topic C, Applications of Right Triangle Trigonometry, students define trigonometric ratios and make connections to the Pythagorean theorem. In this lesson we looked at the relationship between the side lengths of different triangles. Direct link to jinseo.park's post Are special right triangl, Posted 4 years ago. If you create a modified assignment using a purchased editable file, please credit us as follows on all assignment and answer key pages: Use your feedback to make improvements to our products and services and even launch new products and services, with the understanding that you will not be paid or own any part of the new or improved products and services (unless we otherwise agree in writing ahead of time). The hypotenuse is opposite the right angle. When you are done, click on the Show answer tab to see if you got the correct answer. 3 pages. Knowing the vocabulary accurately is important for us to communicate. Thank you for using eMATHinstruction materials. Unit 6 triangles and congruence lesson 1 answer key - Unit 6-Triangles & Congruence. The height of the triangle is 2. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. F.TF.C.8 Lesson 1 Congruent Triangles & CPCTC. Pause, rewind, replay, stop follow your pace! Give students 4 minutes of quiet work time followed by partner and then whole-class discussions. Do all target tasks. Spring 2023, GEOMETRY 10B when working out the inverse trig, is the bigger number always on the bottom? Then calculate the area and perimeter of each triangle. 18 Resources Daily Notetaking Guide 7-5 Daily Notetaking Guide 7-5 Adapted Instruction Closure Learn with flashcards, games, and more - for free. Theanglemade bythelineof sight ofanobserveronthegroundtoapointabovethe horizontaliscalled the angle of elevation. The triangle on the left has the square labels a squared equals 16 aligned to the bottom horizontal leg and b squared equals 10 aligned to the left leg. Direct link to Raghunandan wable's post in question 1.1 the given, Posted 6 years ago. You can make in-house photocopies of downloaded material to distribute to your class. Here is a diagram of an acute triangle . For Example-. when solving for an angle why does cos have a -1 on top? Teachers with a valid work email address canclick here to register or sign in for free access to Cool-Downs. How can you tell if a triangle is a 30 60 90 triangle vs a 45 45 90 triangle? Direct link to David Severin's post No, but it is approximate, Posted 3 years ago. In the first right triangle in the diagram, \(9+16=25\), in the second, \(1+16=17\), and in the third, \(9+9=18\). and and and Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Triangle C, right, legs = 1,8. hypotenuse = square root 65. 8 spiritual secrets for multiplying your money. Fall 2020. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Direct link to seonyeongs's post when solving for an angle, Posted 3 years ago. A right triangle A B C. Angle A C B is a right angle. I'd make sure I knew the basic skills for the topic. Use square root and cube root symbols to represent solutions to equations of the form x = p and x = p, where p is a positive rational number. Help! Determine which length represents ]. The square labeled c squared equals 16 is aligned with the hypotenuse.

, Privacy Policy | Accessibility Information. Standards in future grades or units that connect to the content in this unit. Give an example. . Posted 6 years ago. G.SRT.B.4 10. It is important to note that this relationship does not hold for all triangles. To find a triangle's area, use the formula area = 1/2 * base * height. F.TF.A.1 NO WARRANTY. The whole trick to the question is that zero radians is an answer, and if you look closely, you see that no other answer other than 0*pi/10 will get you there, if zero is a possible answer for n. But then since sin(u) must be 20x, then you must still find an answer for every negative pi and positive pi in addition to finding the answer that will get you to zero, which is one of the possible answers. 1. If you start with x3 = 18, divide both sides by 3 to get x = 18/3, but since we do not like roots in the denominator, we then multiply by 3/3 to get 183/(3*3) = 18 3/3=63. Side A C is unknown. This skill is extended in Topic D, the Unit Circle, where students are introduced to the unit circle and reference angles. Similar Right Triangles To Find Slope Teaching Resources . Use the Pythagorean theorem and its converse in the solution of problems. 1778 0 obj <> endobj Yes 2. A brief review will help you boost your confidence to start the new lesson, and thats perfectly fine. WHY. Posted 6 years ago. That is an interesting point that I hadn't considered, but not what the question is asking. 3 by 6 is 18, and that divided by 2 would equal 9, which is the correct answeer. The trig functions give outputs in terms of the ratios of two sides of a triangle when we feed them the input of an angle measure. Solve applications involving angles of elevation and depression. endstream endobj 1779 0 obj <>/Metadata 152 0 R/Pages 1776 0 R/StructTreeRoot 184 0 R/Type/Catalog>> endobj 1780 0 obj <>/MediaBox[0 0 612 792]/Parent 1776 0 R/Resources<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI]/XObject<>>>/Rotate 0/StructParents 0/Tabs/S/Type/Page>> endobj 1781 0 obj <>stream Use the Pythagorean theorem and its converse in the solution of problems. Practice These are questions on fundamental concepts that you need to know before you can embark on this lesson. Look for and make use of structure. 7.RP.A.2 Let's find, for example, the measure of \angle A A in this triangle: Define angles in standard position and use them to build the first quadrant of the unit circle. Home > INT2 > Chapter 6 > Lesson 6.1.1 > Problem 6-6. . It will help you practice the lesson and reinforce your knowledge. F.TF.A.3 G.SRT.D.10 Triangle F: Horizontal side a is 2 units. Direct link to gracieseitz's post Let's say that there is a, Posted 4 years ago. Direct link to Markarino /TEE/DGPE-PI1 #Evaluate's post Boy, I hope you're still , Posted 5 years ago. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. If you know the hypotenuse of a 30-60-90 triangle the 30-degree is half as long and the 60-degree side is root 3/2 times as long. Encourage groups to divide up the work completing the tables and discuss strategiesto find the rest of the unknown side lengths. Get math help online by chatting with a tutor or watching a video lesson. You should now be ready to start working on the WeBWorK problems. In this warm-up, students compare four triangles. A 45 45 90 triangle is isosceles. If we have a dispute that we cannot resolve on our own, we will use mediation before filing a lawsuit in a regular court (except that we can use small claims court). I use this trick on 30, 60, 90 triangles and I've never gotten a single wrong -. Direct link to AHsciencegirl's post Good point, let's estimat, Posted 3 years ago. Practice set 2: Solving for an angle Trigonometry can also be used to find missing angle measures. A television is usually described by the length of the screen's diagonal. Connexus Connections Academy (Connections Academy Online, MCA), {[ course.numDocs ]} Document{[course.numDocs>1? Sorry, the content you are trying to access requires verification that you are a mathematics teacher. Right Triangle yes Would these three sides form a right angle 8, 15, 17 12 Which side length would be considered c? Connexus Connections Academy (Connections Academy Online, MCA)'s GEOMETRY department has 8 courses in Course Hero with 92 documents and 62 answered questions. Explain and use the relationship between the sine and cosine of complementary angles. Describe the relationship between slope and the tangent ratio of the angle of elevation/depression. Ask students: If time allows, draw a few right triangles withlabeledside lengths marked \(a\), \(b\), and \(c\) and display for all to see. They all different. 10. Where cos(x) would take in an angle and output a ratio of side lengths, cos^-1(x) takes in the ratio of adjacent/hypotenuse and gives you an angle, which is why we use it when solving for unknown angles. . You may not publish or compile downloaded content into the digital equivalent of a bound book. f;XqvFOh| -<5, l"G3bsK}^";@-.;{+\c]sg{VNj~@ZDof HWtt4Tt4pE .i 432libPq0M2aT!rJwTr}x$000``c z \Oi(Yxb@ t Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Description:

A square with side lengths of 14 units on a square grid. THey are the inverse functions of the normal trig functions. The length of the shorter leg of the triangle is one half h units. Using these materials implies you agree to our terms and conditions and single user license agreement. REMEMBER One Pythagorean identity states that sin 2 + cos = 1. Complete each statement with always, sometimes or never. Select 23 groups to share their strategies and the values for the side lengths they found (\(\sqrt{9}=3\), \(\sqrt{10}\), \(\sqrt{25}=5\)). Direct link to NightmareChild's post I agree with Spandan. Right Triangle Connection Page: M4 -55A Lesson: 2. Winter 2019, GEOMETRY UNIT3VOCAB One of the best known mathematical formulas is Pythagorean Theorem, which provides us with the relationship between the sides in a right triangle. Key Words. Math can be tough, but . Solving for Missing Sides of a Right Triangle, Unit #8 Review Right Triangle Trigonometry, Unit 8 Mid-Unit Quiz (Through Lesson #4) Form A, Unit 8 Mid-Unit Quiz (Through Lesson #4) Form B, Unit 8 Mid-Unit Quiz (Through Lesson #4) Form C, Unit 8 Mid-Unit Quiz (Through Lesson #4) Form D, U08.AO.01 Terminology Warm-Up for the Trigonometric Ratios (Before Lesson 2), U08.AO.02 Right Triangle Trigonometry Practice, U08.AO.03 Multi-Step Right Triangle Trigonometry Practice. Direct link to Hecretary Bird's post Trig functions like cos^-, Posted 5 years ago. 1 . If you get stuck, try plotting the points on graph paper. 2016-2017 Congruency, Similarity, Right Triangles, and Trigonometry - Answer Key 3 MAFS.912.G-CO.1.1 EOC Practice Level 2 Level 3 Level 4 Level 5 uses definitions to choose examples and non-examples uses precise definitions that are based on the undefined notions of point, line, distance along a line, and distance around a circular arc Instead, tell students that we are going to look at more triangles tofind a pattern. You would even be able to calculate the height the agent is holding his gun at with stretched arms when you know the angle he's keeping his arms at, his arm length and the length from his shoulders to the ground. The swing ropes are. How do we use our calculator to find an unknown angle in a right triangle if two sides are given? Fall 2020, GEOMETRY UNIT3 Round your answers to the nearest tenth. This is like a mini-lesson with an overview of the main objects of study. If you are a school, please purchase a license for each teacher/user. Multiply and divide radicals. 1836 0 obj <>stream Complete the tables for these three more triangles: What do you notice about the values in the table for Triangle Q but not for Triangles P and R? junio 12, 2022. abc news anchors female philadelphia . %PDF-1.5 % Course Hero is not sponsored or endorsed by any college or university. Ask selected students to share their reasoning. Display the image of the triangle on a grid for all to see and ask students to consider how they would find the value of each of the side lengthsof the triangle. Use the graph to discover how. %%EOF Be prepared to explain your reasoning. Make sure the class comes to an agreement. Congruent Triangles: Triangles that. ). Theorems include: measures of interior angles of a triangle sum to 180; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Problem 1. Use side and angle relationships in right and non-right triangles to solve application problems. Recognize and represent proportional relationships between quantities. They do not have a value outright, it would be like trying to ask what the value of f(x) = x + 1 is. Define and prove the Pythagorean theorem. This is because if you multiply the square root of 3 by 6 times the root of three, that would be the same as multiplying 3 by 6 (because the square root of 3 squared is 3). two smaller right triangles that are formed. Angle B A C is unknown. Notice that for these examples of right triangles, the square of the hypotenuse is equal to the sum of the squares of the legs. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Side A B is seven units. Problem 1 : In the diagram given below, using similar triangles, prove that the slope between the points D and F is the same as the slope . Choose a side to use for the base, and find the height of the triangle from that base . Adaptations and updates to IM 68 Math are copyright 2019by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). 01 - Terminology Warm-Up for the Trigonometric Ratios (Before Lesson 2). If no student brings up the fact that Triangle Bis the only one that is not a right triangle, be sure to point that out. We believe in the quality and value of our products and services, and we work hard to make sure they work well and are free of bugs. G.SRT.D.9 G.SRT.B.5 Tell them we will prove that this is always true in the next lesson. The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics. Hopefully,someone noticedthat \(a^2+b^2 = c^2\) for triangles E and Q and someone else noticed they are right triangles. F.TF.C.9 Many times the mini-lesson will not be enough for you to start working on the problems. - The purpose of this task is for students to thinkabout the relationships between the squares of theside lengths of triangles as a leadup to the Pythagorean Theorem at the end of this lesson. A right triangle A B C where angle A C B is the right angle. The square labeled c squared equals 18 is attached to the hypotenuse.

. Make sense of problems and persevere in solving them. 8.G.B.7 Standards covered in previous units or grades that are important background for the current unit. Direct link to sydney's post How can you tell if a tri, Posted 4 years ago. Side c slants downward and to the right. Howard is designing a chair swing ride. Arrange students in groups of 23. Explain and use the relationship between the sine and cosine of complementary angles. If this doesn't solve the problem, visit our Support Center . For example, in this right triangle, \(a=\sqrt{20}\), \(b=\sqrt5\), and \(c=5\). Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Side b slants upward and to the left. 6. Side A B is labeled hypotenuse. - Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. lesson 1: the right triangle connection answer key. Look for and express regularity in repeated reasoning. The, Posted 6 years ago. A square is drawn using each side of the triangles. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. The hypotenuse of a right triangle is the longest side. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Side B C is two units. Now we evaluate using the calculator and round: A right triangle A B C. Angle A C B is a right angle. A.SSE.A.2 1 2 3 831 Use a separate piece of . Students may point out that for the side that is not diagonal, the square is not needed. Trig functions like cos^-1(x) are called inverse trig functions. A right triangle is. We value your feedback about our products and services. *figures that have the same shape and size. shorter leg Solve for s. s 1.155 Simplify. This is not correct. there is a second square inside the square. G.SRT.C.7 Diagonal side c slants downward and to the right and the triangle has a height of 1 unit. Direct link to David Severin's post Congruent are same size a, Posted 6 years ago. FEEDBACK REQUESTED. Reason abstractly and quantitatively. Trigonometry can be used to find a missing side length in a right triangle. Direct link to John Thommen's post This is not correct. LESSON 3 KEY - GEOMETRY - P.1 - Key A) THE PYTHAGOREAN THEOREM The Pythagorean Theorem is used to find the missing side of a right triangle. Lesson Map Topic A: Right Triangle Properties and Side-Length Relationships 1 Define the parts of a right triangle and describe the properties of an altitude of a right triangle. 7.2 Right Triangle Trigonometry - Algebra and Trigonometry 2e | OpenStax File failed to load: https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/jax/element/mml/optable/BasicLatin.js Uh-oh, there's been a glitch We're not quite sure what went wrong. Direct link to Thien D Ho's post Look at the formula of ea, Posted 2 years ago. If the legs are , then. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. hypotenuse leg leg right angle symbol 1. Verify experimentally the properties of rotations, reflections, and translations: 8.G.A.4 If the short leg (the opposite leg to ) is , then, Special Triangle: This is a triangle whose angles are , and . If you need to purchase a membership we offer yearly memberships for tutors and teachers and special bulk discounts for schools. The Sine, Cosine, and Tangent are three different functions. The triangle on the left has the square labels a squared equals 16 and b squared equals 9 attached to each of the legs.

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