Similar triangles worksheet

Similar triangles worksheet

Use this handy Similar Triangles Worksheet to save preparation time and help your children calculate angles of isosceles, scalene and right-angled triangles. It allows …The sides of a triangle measure 3 cm, 5 cm, and 6 cm. If the side of a similar triangle corresponding to 3 cm measures 8 cm, a) draw a diagram, then determine the lengths of the other sides. b) determine the ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle. Triangles CDE and NOP are similar. Use this handy Similar Triangles Worksheet to save preparation time and help your children calculate angles of isosceles, scalene and right-angled triangles. It allows children to practice the skills of calculating angles, while assessment is made easy with the included answer sheet. This Similar Triangles Worksheet includes one page of clearly organised triangle problems, and another answer ... Problems 3. The two triangles are similar and the ratio of the lengths of their sides is equal to k: AB / A'B' = BC / B'C' = CA / C'A' = k. Find the ratio BH / B'H' of the lengths of the altitudes of the two triangles. Solution to Problem 3. If the two triangles are similar, their corresponding angles are congruent. These similarity and congruence worksheets provide pupils with two different ways to test their understanding. Pupils can practise proving that two or more triangles are similar, and apply similarity to find unknown side lengths. The similarity and congruence worksheets ask them to determine whether pairs of triangles are congruent in ...©5 g250 Q102m RKcu ptja J pS ho pfNt Cw1avr Ae9 KLaL pC 5.z X fAZlsl i 8r micg bh2tFst 5rResZezrBv9eNdn.C u KMHamdwe5 nwji9tGhK JI 1nDf7i VnGiNtpe J 5GMeXo0m 4e 4tCrNyr. q Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name_____ Similar Right Triangles Date_____ Period____Triangles EFG and QRS are similar. The length of the sides of EFG are 144, 128, and 112. The length of the smallest side of QRS is 280, what is the length of the longest side of QRS? (draw a diagram and solve) 4. A 40 -foot flagpole casts a 25 foot shadow. Find the shadow cast by a nearby building 200 feet tall. (draw a diagram and solve) 5.T Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Similar Figures Date ... Similar Figures Date_____ Period____ Each pair of figures is similar. Find the missing side. 1) 20 12 x 3 5 2) x 1 9 3 3 3) 4 x 16 8 2 4) 4 5 8 x 10 5) x 14 1 2 7 6) 6 9 24 x 36Course: High school geometry > Unit 4. Lesson 3: Solving similar triangles. Solving similar triangles. Solve similar triangles (basic) Solving similar triangles: same side plays different roles. Solve similar triangles (advanced) Math …Angles. Triangles. Medians of triangles. Altitudes of triangles. Angle bisectors. Circles. Free Geometry worksheets created with Infinite Geometry. Printable in convenient PDF format.A) Find the scale factor of each pair of similar triangles. B) Find the scale factor of each pair of similar triangles. 1) Scale factor of A to B is 2) 3) Scale factor of G to F is 4) 5) Scale factor of P to Q is Scale factor of Q to P is 6) 7) Scale factor of U to V is 2 : 1 4 : 1 1 : 3 3 : 1 5 : 2 Scale factor of V to U is 2 : 5 8) Scale ...The animations are great. Similar Triangles Using Slope - This self-directed activity is a different spin on similar triangles by using slope. Similarity and Proportions Stations Maze Activity - This activity is a stations activity that is a fun way to help students practice multiple choice questions. Similar Figures Cut and Paste Activity ...Angles. Triangles. Medians of triangles. Altitudes of triangles. Angle bisectors. Circles. Free Geometry worksheets created with Infinite Geometry. Printable in convenient PDF format.Classifying triangles worksheets. Triangles are generally classified by their sides (scalene, equilateral, isosceles) and / or their angles (acute, obtuse, right) angles. In these geometry worksheets, students classify angles and learn the related terminology. Classify by angles: Worksheet #1. Classify by sides:This printable Similar Triangles worksheet is a great resources for the 6th, 7th and 8th Grade. Similar Triangles Worksheets with Answers PDF. <style>.woocommerce-product-gallery{ opacity: 1 !important; }</style>if the sides of two similar triangles are in the ratio 4 : 9, then the areas of these triangles. free mathematics worksheets with answer keys can be found on ...For similar triangles A B C and X Y Z shown below: X Y = k ( A B) Y Z = k ( B C) X Z = k ( A C) X Y A B = Y Z B C = X Z A C = k. A B C X Y Z. To calculate a missing side length, we: Write a proportional relationship using two pairs of corresponding sides. Plug in known side lengths. We need to know 3.Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; October 7, 2019 October 9, 2023 corbettmaths. Similar Shapes: Finding Sides Textbook …Similar Triangles. Worksheets. Number Line Subtraction Worksheets. Order of Operations with Fractions Worksheets. ... Isosceles and Equilateral Triangles Worksheets. Classifying Triangles Worksheets. Angles in a Triangle Worksheets. Area of Triangles and Trapezoids Worksheets.9. In the diagram below, Mr. Wontit is staring at a point C that creates two similar triangles as shown in the diagram below: a) Based on the diagram, how far is the bottom of the tree from the point C on the ground? 10. In the diagram below, …This extensive collection of worksheets on triangles for grades 3 through high-school is incredibly useful in imparting a clear understanding of a variety of topics like classifying triangles, similar triangles, congruence of triangles, median and centroid of a triangle, inequality theorem, Pythagorean inequalities, area, perimeter and angles in...The triangles in each pair are similar. 11) 65 9 x + 6 R F Q 143 132 F G H A) 9 B) 10 C) 14 D) 6 ... Similar Triangle worksheet Created Date: 11/20/2014 2:24:53 AM ...PPT. Standard. PDF. Small. PDF. Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes.We can find the areas using this formula from Area of a Triangle: Area of ABC = 12 bc sin(A) Area of PQR = 12 qr sin(P) And we know the lengths of the triangles are in the ratio x:y. q/b = y/x, so: q = by/x. and r/c = y/x, so r = cy/x. Also, since the triangles are similar, angles A and P are the same: A = P. We can now do some calculations:Similar Figures 1 Introduction Similar triangles are fundamentals of geometry. Without them, it would be very di cult in many con gurations to convert angle information to length information (e.g. through AA similarity) and vice versa. At the same time, though, similar triangles are often the most di cult things to spot without prior geometric ...For most my life, I had no idea what emotions were, why they were necessary, or what I was supposed to do with For most my life, I had no idea what emotions were, why they were necessary, or what I was supposed to do with them. I made all s...Euclidean geometry. 1 Classification of triangles. 2 Congruency. 4 The theorem of Pythagoras. Two triangles are congruent if one fits exactly over the other. This means that the triangles have equal corresponding angles and sides. To determine whether two triangles are congruent, it is not necessary to check every side and every angle.In this video, learn how similar triangles can be used to help explain the concept of slope. In the accompanying classroom activity, students apply the ...Similar Triangle Worksheet 1. State whether or not the following triangles are similar and support your answer. 2. (i) Determine if the triangles below are similar, and explain how you know. (ii) Find the lengths of the missing sides. All measures are centimeters unless otherwise stated. a) b) 5 3 1 a 2 0 1 5 1 2 b c) d 4 m 5 m 15Our Geometry Similar Triangles Quiz with Answers is a versatile resource that can be used for several Australian content descriptors including: Year 6 AC9M6M04: Identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning; Year 6 ...Mathster keyboard_arrow_up. Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers. Worksheet Name. 1. …Two triangles are Similar if the only difference is size (and possibly the need to turn or flip one around). These triangles are all similar: (Equal angles have been marked with the same number of arcs) Notice that, as …State whether the two triangles are similar. Give a reason to support your answer. No. Two of the sides of the triangle are increased by a scale factor of 1.5. The other side has been increased by ...Use the similar triangles to find the height of the telephone pole. 2. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost? 25 feet 20 feet 8 ft 6 ft x 15 ft Your Turn: DefinitionLesson: Similarity of Triangles Mathematics • Class X. Lesson: Similarity of Triangles. In this lesson, we will learn how to determine and prove whether two triangles are similar using equality of corresponding angles or proportionality of corresponding sides and how to use similarity to find unknown lengths and angles. Exploring Similar Figures Similar Figures — Polygons that have the same shape, but different size. Corresponding — Having the same position. Two polygons are similar if: 1. corresponding angles are congruent AND 2. the lengths of corresponding sides are in proportion, called the scale factor. Show if the triangles below are similar or not. Worksheets. Triangle Worksheets; Rectangle Worksheets; Circle Worksheets; ... Integers Worksheets; Factors Worksheets; Equivalent Ratios Worksheets; Counting Worksheets; ... I want to know where are the answers for the worksheets. Thank you. Reply. staff says: May 4, 2023 at 4:12 pm.Feb 13, 2017 · A worksheet on finding missing angles and sides in similar triangles. Kuta Software Worksheets always has well-designed worksheets with plenty of white space and progressively more difficult problems! The similar figures worksheet contains only triangles. But gives students practice identifying similarity by proportion. It’s a good fit for middle and high school students. This one is free and …©4 C2p0s1 Z2e kKau btva o tS uo cfht 8wBaqr Net 8L zL sC C.Z x CA7lYl m Ur Ci Bgvh 9tVs6 ZrbeksTeHr uvZexdM.1 e QMGabd 6e0 Lw di Vtch d VIen2f li knZintfe h fP nr LeL- iAglwgweqb BrkaB.8 Worksheet by Kuta Software LLC Find the slope of the line through each pair of points. 9) ( , ), ( , )Finding free printable worksheets is an excellent way for teachers and homeschooling parents to save on their budgets. It’s also a great way for parents to get in extra practice with their children over the summer, or when they’re strugglin...Give your students extra practice or assess their knowledge of identify the Altitude and Leg Rule when working with similar right triangles with this card sort. Students will also solve each problem. There are 4 problems total. Download includes both 8.5 x 11 worksheet and interactive notebook versions of activity.Step 2: The corresponding sides that involve x are A B = 30 and E D = x, so we form the ratio of them and set it equal to the ratio found in Step 1: 30 x = 15 6. Step 3: Cross-multiplying and ...1) Angle-Angle (AA) Rule. It states that if two angles in one triangle are equal to two angles of the other triangle, then the two triangles are similar. From the above figure with AA rule, we can write. AB/EF = BC/FG = AC/EG and ∠B ≅ ∠F. Thus, to prove two triangles are similar, it is sufficient to show that two angles of one triangle ...The similar triangles worksheets provide practice in determining the scale factors, identifying similar triangles, calculating side lengths, writing the similarity statements; …The best source for free math worksheets. Printable or interactive. Easier to grade, more in-depth and 100% FREE! Kindergarten, 1st Grade, 2nd Grade, ...Name: _____ Geometry AB Worksheet 6-6 – Overlapping Similar Triangles Find x in each figure (assume the segment across the triangle is parallel to the third side):©N W2h0 S1P12 6K Pu CtcaN TS woPfytzw ya Jr de F 0L2LfCN.M p PAsl l0 qr hiUgjhWtTs 2 CrmexsUeDrsv deOdn.V 3 sMia bd3e e aw7iStzh y EIn1fpi Ensizt3e 5 LG1eXodm YehtDrJy w.W Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name_____ Using Similar Polygons Date_____ Period____The triangles in the Navajo rug look similar. To show that they are similar, you can use the definition of similar polygons or the AA Similarity Postulate. In this lesson, you will learn two new methods to show that two triangles are similar. 7.4 Showing Triangles are Similar: SSS and SAS Determine whether the triangles are similar. If they are ...Triangles Class 10 MCQs Questions with Answers. Question 1. In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is: Question 2. Triangles Class 9 Practice Set 3.1 solved problems are more helpful to your preparation.Class 10 Maths Chapter 6 Triangles Questions for Practice. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.. Introduction to triangle similarity Determine similar triangles: Angles Google Classroom Which triangles are similar to A B C ? 58 ° 68 ° A B C Choose 1 answer: 54 ° 93 ° Q R S Q R S only A 54 ° 93 ° Q R S Q R S only 58 ° 54 ° T U V T U V only B 58 ° 54 ° T U V T U V only Both C Both Neither D Neither Do 4 problemsUse this handy Similar Triangles Worksheet to save preparation time and help your children calculate angles of isosceles, scalene and right-angled triangles. It allows children to practice the skills of calculating angles, while assessment is made easy with the included answer sheet. This Similar Triangles Worksheet includes one page of clearly organised triangle problems, and another answer ... Write whether each pair of triangles are similar. d d d d d d in in in 16 in 20 in 18 in t t t t t t 10 in 9 in 11 in 30 in 27 in 33 in t t 26 t t t t d d d d d d 3) 5) 7) 1) 4) 6) 8) 2) 2 in 3 in 4 in 4 in 6 in 8 in t t t t t t Similarity of Triangles Sheet 1 Name : Printable Worksheets @ www.mathworksheets4kids.com Objective: This lesson is designed to help you discover the properties of similar triangles and to specifically understand the concept of proportionality. You will be determining the general conditions required to verify or prove that two triangles are similar. 1. List all Triangle Congruence Postulates that you know. There are five!These worksheets explains how to determine if triangles and similar and how to use similarity to solve problems. Your students will use these activity sheets to identify similar triangles by applying the correct proofs, as well as calculate segment lengths. Students should already be familiar with the applicable proofs and formulas. BEC and DCF are equilateral triangles. (a) Prove that triangle ECD is congruent to triangle BCF. (3) G is the point such that BEGF is a parallelogram. (b) Prove that ED = EG (2) (5 marks) 5. B. A C. D Diagram NOT accurately drawn. In the diagram, AB = BC = CD = DA. Prove that triangle ADB is congruent to triangle CDB. (3 marks) 6. AClass 10 Maths Chapter 6 Triangles Questions for Practice. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.Worksheet Overview. Triangles that have exactly the same angles are similar. If two angles match, the third angle will automatically match as the angle sum is ...The fixed ratio of distances between two similar figures can be referred to as the. Similarity tests for triangles. It is worth noting that, since all triangles have a fixed angle sum of 180^ { \circ {}} having two matching angles is equivalent to having three matching angles. To determine which sides are corresponding in two potentially ... Students will begin to identify similar triangles, using the conditions of similarity and calculate missing lengths in pairs of similar triangles with this worksheet. Section A consists of four sets of three triangles. Learners must identify the pair of similar triangles as well as stating the condition for similarity. In section B, students ...This worksheet explains how to find the measure of the side of a triangle given the measurements of a similar triangle. A sample problem is solved, and two practice problems are provided. Practice Worksheet We learn how to apply this skill to real world word problems such as: At a certain time of the day, the shadow of a 9' boy is 14' long.©L G2F0R1z2 9 8K2u8t oaP dS RoWfQtuwQagrie k RLSLhC 0.m Y qA5l4l5 SrBi8guh BtQsl zryeOs6edr 0vHeKdv.I E rM Bamdte J bw 1i 0t KhK tI enGfViCn FiStDep KPKrAe4- YALltgfe gb Wr7a b.S Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Similar Figures Date_____ Period____ Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance A worksheet on finding missing angles and sides in similar triangles.Lesson: Similarity of Triangles Mathematics • Class X. Lesson: Similarity of Triangles. In this lesson, we will learn how to determine and prove whether two triangles are similar using equality of corresponding angles or proportionality of corresponding sides and how to use similarity to find unknown lengths and angles.The fixed ratio of distances between two similar figures can be referred to as the. Similarity tests for triangles. It is worth noting that, since all triangles have a fixed angle sum of 180^ { \circ {}} having two matching angles is equivalent to having three matching angles. To determine which sides are corresponding in two potentially ...Use this handy Similar Triangles Activity Worksheet to save preparation time and help your children calculate angles of isosceles, scalene and right-angled triangles. It allows …This is a digital activity. It is a color-by-number puzzle in Google Sheets. There are 12 questions/diagrams and students will solve the missing side of similar right triangles using Geometric Mean. As the students answered the questions correctly the box turns green and part of the picture is being colored. If they answered incorrectly the box ...This worksheet explains how to find the measure of the side of a triangle given the measurements of a similar triangle. A sample problem is solved, and two practice problems are provided. Practice Worksheet We learn how to apply this skill to real world word problems such as: At a certain time of the day, the shadow of a 9' boy is 14' long.These Similarity Worksheets will produce eight problems for working with similar triangles. You may select whether to include non-similar triangle pairs, as well as the type of similarity in each pair. These worksheets are a great resources for the 5th, 6th Grade, 7th Grade, 8th Grade, 9th Grade, and 10th Grade. Similar Right Triangles Worksheets.Investigating Similar Triangles Activity (Editable Word | PDF | Answers) Sine, Cosine and Tangent Ratios Fill in the Blanks (Editable Word | PDF | Answers) Which Trigonometric Ratio Practice Strips (Editable Word | PDF | Answers) Find Angles Using Trigonometry Practice Strips (Editable Word | PDF | Answers)16. Ryan and Kathy each drew a triangle with an angle of 20 degrees. Under which condition would the triangles be similar? a) if both are right triangles. b) if both are obtuse triangles. c) if the triangles have the same area. d) if the triangles have the same perimeter. Y. X. 6 in. G. F. 2 in. Z. W. H. E. 3 in. 5 ft. 32 ft. 8 ft. X? L. Y. W ...Similar Triangle Worksheet 1. State whether or not the following triangles are similar and support your answer. 2. (i) Determine if the triangles below are similar, and explain how you know. (ii) Find the lengths of the missing sides. All measures are centimeters unless otherwise stated. a) b) 5 3 1 a 2 0 1 5 1 2 b c) d 4 m 5 m 15WORD PROBLEMS INVOLVING SIMILAR TRIANGLES WORKSHEET. Problem 1 : A ramp is built enable wheel-chair access to a building that is 24 cm above ground level. The ramp has a constant slope of 2 in 15, which means that for every 15 cm horizontally its rises 2 cm. Calculate the length of the base of the ramp. Solution.STEP 3. Find the Scale Factor from two known lengths, areas or volumes. Second Quantity ÷ First Quantity. Check the scale factor is > 1 if getting bigger and < 1 if getting smaller. If the scale factor, s.f., is from two lengths, write it as k = s.f. If the scale factor, s.f., is from two areas, write it as k 2 = s.f.Angles. Triangles. Medians of triangles. Altitudes of triangles. Angle bisectors. Circles. Free Geometry worksheets created with Infinite Geometry. Printable in convenient PDF format. Which set of dimensions would produce a similar figure? A. 17.6 cm, 88 cm B. 70.4 cm, 176 cm C. 105.6 cm, 132 cm D. 140.8 cm, 220 cm 16. In triangle STR , and are parallel. If SQ = 6 units, QT = 24 units, and the perimeter of triangle SQP is 20 units, what is the perimeter of triangle STR ? A 80 units B 100 units C 320 units D 500 units 17. This collection of printable worksheets assists the 7th grade, 8th grade, and high school students in comprehending scale factor of similar figures. Few instances of real-life application of scale factor are creating miniature models, blueprints and engineering designs. An array of skills like drawing new shapes, enlarge (up scale) or reduce ...4.02 Similar triangle tests. Lesson · Worksheet · Practice. Lesson. Share. Introduction. Two triangles are considered to be similar if one of them can be scaled ...Comprehend how the scale factor impacts side lengths, perimeters and areas of similar shapes with this gamut of scale factor worksheets. Also, learn to find the ratio of areas and perimeters of similar polygons. The worksheets are available in both customary and metric units. The pdf worksheets are recommended for 7th grade, 8th grade, and high ...These two triangles are not similar. The sides lengths of the triangles are not in the same ratio and so the triangles are not similar. For two triangles to be similar, they must have the same internal angles, as shown in the similar shapes below. 3 cm 2 cm 9 cm 6 cm 6 4 5 3 5 4 7.71 6 3.92 50˚ 100˚ 30˚ 100˚ 30˚ 50˚ 15.42 7.84 12Similar Triangles Worksheets. Tags: 5th Grade 6th Grade. The similarity of triangles, like their congruency, is an important concept of geometry. Click on the below images to test yourself on the properties of similar triangles. Download PDF. Download PDF.Similarity Worksheet State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. 1) 16 14 12 K M L 24 18 21 Q R S QRS ~ _____ similar; SSS similarity; KLM 2) 18 12 F E 19 27 K L J JKL ~ _____ not similar 3) M N T S R RST ~ _____ similar; AA similarity; RMN 4) 55 60 63° B C ...Teachers for Teachers worksheets are a great way to provide students with engaging and educational activities. With the right approach, these worksheets can be used to help students learn and retain information in an effective way. Here are...In geometry, a triangle is a shape that consists of a set of three straight lines or sides, three interior angles that are formed by a pair of sides, and three vertices or intersection points of the lines forming the triangle. A triangle can also have an exterior angle. This occurs when we extend one side of a triangle and take the angle the ...Similar Figures 1 Introduction Similar triangles are fundamentals of geometry. Without them, it would be very di cult in many con gurations to convert angle information to length information (e.g. through AA similarity) and vice versa. At the same time, though, similar triangles are often the most di cult things to spot without prior geometric ...Introduction to triangle similarity © 2023 Khan Academy Terms of use Privacy Policy Cookie Notice Determine similar triangles: Angles Google Classroom Problem Which triangles are similar to A B C ‍ ? Triangle A B C. Angle A is fifty-eight degrees. Angle B is sixty-eight degrees. Choose 1 answer: Choose 1 answer: (Choice A) Q R S ‍ only A 16. Ryan and Kathy each drew a triangle with an angle of 20 degrees. Under which condition would the triangles be similar? a) if both are right triangles. b) if both are obtuse triangles. c) if the triangles have the same area. d) if the triangles have the same perimeter. Y. X. 6 in. G. F. 2 in. Z. W. H. E. 3 in. 5 ft. 32 ft. 8 ft. X? L. Y. W ... For most my life, I had no idea what emotions were, why they were necessary, or what I was supposed to do with For most my life, I had no idea what emotions were, why they were necessary, or what I was supposed to do with them. I made all s...16 oct. 2021 ... Answer ... Answer: Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion ...Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents. Similar Triangles. Two triangles are Similar if the only difference is size (and possibly the need to turn or flip one around). These triangles are all similar: (Equal angles have been marked with the same number of arcs)Properties of similar triangles are given below, Similar triangles have the same shape but different sizes. In similar triangles, corresponding angles are equal. Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides.This is a digital activity. It is a color-by-number puzzle in Google Sheets. There are 12 questions/diagrams and students will solve the missing side of similar right triangles using Geometric Mean. As the students answered the questions correctly the box turns green and part of the picture is being colored. If they answered incorrectly the box ... ---1

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