# parallelogram opposite angles theorem

Both pairs of opposite angles are congruent. By the Alternate Interior Angles Theorem, ZADB < (select) and ZABD = (select). Therefore, the difference between the opposite angles of a parallelogram is: x −x = 0∘ x − x = 0 ∘ y −y = 0∘ y − y = 0 ∘ Using the Line Tool, draw line AB. There are four ways to do this. Now, let's recap what we've learned. There is a theorem in a parallelogram where opposite angles are equal. 1 4 2 3. Parallelograms. THEOREM: If a quadrilateral has consecutive angles which are supplementary, then it is a parallelogram. CCSS.MATH.CONTENT.HSG.CO.C.11 Prove theorems about parallelograms. Because we have two pairs of equal and parallel opposite sides, the diagonals will bisect each other. Why don't you try it? Hence, it is proved that the opposite angles of a parallelogram are equal. The opposite sides of a parallelogram are congruent. 1) ∠ 1 = 78° Its opposite angle = 78° (Theorem A) Measure each angle of the other pair of opposite angles (Theorem B): = 180 - 78 = 102° Enrolling in a course lets you earn progress by passing quizzes and exams. A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. Extend segment JM beyond point and draw point P (Construction) ∠ MLK ≅ ∠ PML ( Alternate Interior Angles Theorem) Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Theorem 6.2C states: If both pairs of opposite _____ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 5) Theorem 6.2C states: If both pairs of opposite _____ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 8.5 If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. just create an account. You can conclude that AABD = (select) by the ASA Triangle Congruence Theorem, and so, ZA – 4 (select)y by CPCTC. In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. Opposite sides are congruent. Parallelogram Theorems 3 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. The opposite internal angles of a parallelogram are equal and the adjacent angles are supplementary i.e., the sum of the adjacent angles should be equal to 180 degrees. Opposite angels are congruent (D = B). Alternate interior angles theorem you parallelograms opposite angles are congruent geometry help discussion section 1 3 discussion section 1 3. Sum of adjacent angles of a parallelogram is equal to 180 degrees. 3. Just like we have two pairs of opposite sides, we have two pairs of opposite angles. Conflict Between Antigone & Creon in Sophocles' Antigone, Quiz & Worksheet - Metaphors in The Outsiders, Quiz & Worksheet - Desiree's Baby Time & Place, Quiz & Worksheet - The Handkerchief in Othello. Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent). If you took a ruler and measured each pair, you will see that each pair is the same length. Opposite angles are congruent As you drag any vertex in the parallelogram above, note that the opposite angles are congruent (equal in measure). To learn more, visit our Earning Credit Page. If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram. CCSS.MATH.CONTENT.HSG.CO.C.11 Prove theorems about parallelograms. The adjacent angles form supplementary angles that add up to 180 degrees. Anyone can earn Visually defined, a parallelogram looks like a leaning rectangle. In a parallelogram, the opposite sides and opposite angles are equal. Opposite sides of a parallelogram are equal; we can prove this using the alternate interior angles theorem. Whats people lookup in this blog: Alternate Interior Angles Theorem Parallelogram; Converse Of Alternate Interior Angles Theorem Parallelogram Many of these statements are the converse statements of the proofs we came up with already. Opposite angels are congruent (D = B). Theorem B: Consecutive angles are supplementary (their sum is 180°). Parallelogram Opposite Angles Theorem If a quadrilateral is a parallelogram, then its opposite angles are _____. Services. Solution: For part a, the opposite angles are equal, so by the Opposite Angles Theorem Converse, is a parallelogram. The first is that the opposite angles are equal to each other. Example 1 proves an additional way to show that a quadrilateral is a parallelogram. So we know that AC is parallel to BD by alternate interior angles. Theorem: Visual Representation: Write your questions here! One property that is included in the definition is that the opposite sides are parallel. ABCD is a parallelogram. The opposite internal angles of a parallelogram are equal and the adjacent angles are supplementary i.e., the sum of the adjacent angles should be equal to 180 degrees. A parallelogram is a quadrilateral with opposite sides parallel. For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. A parallelogram has two pairs of opposite sides that are parallel and equal in length. All rights reserved. As you can see, neither of these pairs of lines will ever meet each other. Calculate certain variables of a parallelogram depending on the inputs provided. This means that all three angles in both triangles have the same measure. You can use these and other theorems in this lesson to prove that a quadrilateral with certain properties is a parallelogram. 's' : ''}}. Theorem: Prove that the opposite angles of a parallelogram are equal. Note for example that the angles ∠ABD and ∠ACD are always equal no matter what you do. Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Then find the lengths of the two diagonals of the parallelogram. Opposite angles are congruent As you drag any vertex in the parallelogram above, note that the opposite angles are congruent (equal in measure). lessons in math, English, science, history, and more. Statements of parallelogram and its theorems 1) In a parallelogram, opposite sides are equal. By ASA congruence criterion, two triangles are congruent to each other. Angles ABC and CDA are corresponding parts of congruent triangles, which are congruent (CPCTC). Opposite angles of parallelogram are equal (D = B). Measuring the Area of a Parallelogram: Formula & Examples, Quiz & Worksheet - Properties and Proof Theorems of Parallelograms, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, Measuring the Area of a Rhombus: Formula & Examples, Rectangles: Definition, Properties & Construction, Measuring the Area of a Rectangle: Formula & Examples, Biological and Biomedical Our mathematical definition of a parallelogram includes two inherent properties. If the diagonals of a quadrilateral bisect each other then it is a parallelogram. the Parallelogram Opposite Angles Theorem to prove statements about the sides and angles of the parallelogram. The following is an incomplete flowchart proving that the opposite angles of parallelogram jklm are congruent: which statement and reason can be used to fill in the numbered blank spaces? What Can You Do With a PhD in Educational Psychology? To find s, theorem 14-A states that the opposite sides of a parallelogram are congruent. succeed. Write down a formula for the height of the parallelogram in terms of the cross-product, and deduce a formula for the area of the parallelogram. Visit us at - www.risingpearl.comLike us at - www.facebook.com/risingpearlfansFriends,This is a Math video. First day back from Christmas break saw my Geometry classes looking at theorems about parallelograms and rhombuses. Parallelograms have two properties related to their angles. - Definition, Properties, Types & Examples, Proving That a Quadrilateral is a Parallelogram, Simplifying Expressions with Rational Exponents, Isosceles Trapezoid: Definition, Properties & Formula, Angles of Elevation & Depression: Practice Problems, Properties of Shapes: Rectangles, Squares and Rhombuses, GRE Quantitative Reasoning: Study Guide & Test Prep, SAT Subject Test Mathematics Level 2: Practice and Study Guide, High School Geometry: Homework Help Resource, Ohio Graduation Test: Study Guide & Practice, SAT Subject Test Chemistry: Practice and Study Guide, SAT Subject Test Biology: Practice and Study Guide. 8) Theorem 6.3E states that if two congruent angles are _____, then each angle is a right angle. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons courses that prepare you to earn So we know that AC is parallel to BD by alternate interior angles. Consider the following figure: Proof: In $$\Delta ABC$$ and $$\Delta CDA$$, \[\begin{align} Answers: 3 Show answers Another question on Mathematics. Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz, Visit BYJU’S for all Maths related queries and study materials, Your email address will not be published. If one angle is right, then all angles are right. Since, the adjacent sides are supplementary. The diagonals are the lines that connect the opposite corners to each other. We’d already looked at definitions of the different types of special quadrilaterals. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. How do you know? If the measure of angle A is 60, then what is the measure of angle C? The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Theorem 6.2C states: If both pairs of opposite _____ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Try it for yourself. Prove: ∠ MLK ≅ ∠ KJM and ∠ JML ≅ ∠ LKJ. If you look at each pair of opposite sides and drew the lines out, you would find that these lines will never meet. Ways To Prove A Quadrilateral Is A Parallelogram Teaching The Lesson Teaching Quadrilaterals Lesson . Classify quadrilateral as parallelogram a classic activity. angles If an angle of a quadrilateral is supplementary to both of its _____ angles, then the quadrilateral is a parallelogram. Parallelograms have two properties related to their angles. The goal is to prove that the opposite angles are congruent. Each diagonal of a parallelogram separates it into two congruent triangles. One pair can be longer than the other. The diagonals of a parallelogram … Proof. Then the lengths of the two diagonals of, Draw a picture of a parallelogram with two sides a and b. Put your understanding of this concept to test by answering a few MCQs. Supplementary angles are two angles adding to 180°. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Draw a generic parallelogram and preview the proof. Alternate Interior Angles Theorem Step-by-step explanation: Here, Given: JKML is a parallelogram, That is, JK ║ ML and JM ║ KL. Below, we can label one pair of angles with a and the other pair with b. Further, the following statements are all equivalent (if one is true, so are all the others): You can combine the top two, the bottom two, the left two, or even the right two. To show these two triangles are congruent we’ll use the fact that this is a parallelogram, and as a result, the two opposite sid… parallelogram theorem ; THEOREM – 1 A diagonal of parallelogram divides it into two triangles of equal area. Opposite Angles Theorem Converse: If both pairs of opposite angles of a quadrilateral are congruent, then the figure is a parallelogram. Create your account. Parallelogram Theorems 4 Log in here for access. We've shown if you have a parallelogram, opposite sides have the same length. A parallelogram is a quadrilateral with opposite sides parallel. When the angles of the parallelogram equal to 90 degrees, it forms a rectangle. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Theorem 1. We know this is a parallelogram so the two opposite sides are parallel, and the diagonal acts as a transversal line, intersecting both pairs of parallel lines - hinting we should use the Alternate Interior Angles Theorem. See Interior angles of a polygon. For example, ∠A, ∠B are adjacent angles and ∠A = 90°, then: In the adjoining figure, ∠D = 85° and ∠B = (x+25)°, find the value of x. The diagonals bisect each other. Properties of a Parallelogram. Click ‘Start Quiz’ to begin! The point where they bisect is exactly the halfway point of each diagonal. Opposite Angles of a Parallelogram are Equal. © copyright 2003-2021 Study.com. Sciences, Culinary Arts and Personal A quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, then the quadrilateral is called a parallelogram. Th… the Parallelogram Opposite Angles Theorem to prove statements about the sides and angles of the parallelogram. The diagonals of a parallelogram bisect each other. The diagonals of a parallelogram bisect each other. A parallelogram however has some additional properties. I had students divide a page in their notebook in two, and told them to rewrite the definitions of the parallelogram and rhombus in those sections. (Proof of theorem appears further down page.) Solve for s, t, v, w, and x.Also determine the measure of angle LMN. The second is that a pair of adjacent angles will always add up to 180 degrees. Construct line BC, then construct a line parallel to BC through point A. credit-by-exam regardless of age or education level. imaginable degree, area of Name_____ Must pass MC by:_____ If a quadrilateral is a parallelogram, then its opposite sides are congruent. Parallelogram Diagonals Converse If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. We don't have to check to make sure all the properties are there. Theorems of Quadrilateral Shapes 1. | {{course.flashcardSetCount}} In a parallelogram, any two consecutive angles are supplementary, no matter which pair you pick. The converses of the theorems are stated below. Not sure what college you want to attend yet? So this is parallel to that. 3.™1 £ ™3 3. If one angle is right, then all angles are right. Do they look like they will meet? Theorem 1: Opposite sides are congruent. AREA: Find a number \displaystyle a so that the change of variables \displaystyle s=x+ay,\ \ t=y transforms the integral \displaystyle \int\int_R \ dx\ dy over the parallelogram \displaystyle R in the \disp, Find the area of the parallelogram determined by the vectors \mathbf{v} and \mathbf{w} where \mathbf{v} = 2 \mathbf{i} + 3 \mathbf{k} and \mathbf{w} = 2 \mathbf{j} - 3 \mathbf{k}, Working Scholars® Bringing Tuition-Free College to the Community, You have two pairs of parallel opposite sides, You have two pairs of equal opposite angles, You have two pairs of equal and parallel opposite sides, It has two pairs of parallel opposite sides, It has two pairs of equal opposite angles, It has two pairs of equal and parallel opposite sides, Discuss the particulars of parallelograms, supplementary angles and proof theorems, Provide characteristics of the angles of parallelograms, List the criteria required to identify a parallelogram. Each diagonal of a parallelogram separates it into two congruent triangles. The important properties of angles of a parallelogram are: In the above parallelogram, A, C and B, D are a pair of opposite angles. It's as if a rectangle had a long, busy day and is now just resting and leaning up against a wall. Alternate interior angles parallelogram. - Definition and Properties, Parallelogram in Geometry: Definition, Shapes & Properties, Kites in Geometry: Definition and Properties, Solving Quadratic Inequalities in One Variable, Angle Bisector Theorem: Definition and Example, What is a Quadrilateral? So, if we went around clockwise starting from the top left angle, we would see a, b, a, and then b again. To get another theorem for parallelograms, let's prove that the opposite angles of a parallelogram are congruent. Select a subject to preview related courses: Now that we know the properties that make up a parallelogram, it becomes easy to identify a parallelogram. Also, the opposite sides are equal in length. Let’s use congruent triangles first because it requires less additional lines. If a quadrilateral is a parallelogram, then its Angles, Parallelogram This shows that the opposite sides of a parallelogram are always equal in length and the opposite angles are also equal. All other trademarks and copyrights are the property of their respective owners. A parallelogram also has two pairs of opposite angles that are also equal to each other. Parallelogram Diagonals Theorem If a quadrilateral is a parallelogram… Visit the Geometry: High School page to learn more. What this means is that a parallelogram has two pairs of opposite sides that are parallel to each other and are the same length. And if opposite sides have the same length, then you have a parallelogram. Opposite sides of parallelogram are equal (AB = DC). 2. One pair of opposite sides is both congruent and parallel. parallelogram theorems. A parallelogram however has some additional properties. Theorem 4. We know that interior angles on the same side of a transversal are supplementary. How Do I Use Study.com's Assign Lesson Feature? You will see the unique properties that belong to the parallelogram. {{courseNav.course.topics.length}} chapters | Write and… What is the Main Frame Story of The Canterbury Tales? As a member, you'll also get unlimited access to over 83,000 Example 2: Given .LMPN. Through point C, (C not on line AB) draw a second line, parallel to AB. Given 2.™1 £ ™2, ™2 £ ™3 2. 1. Watch this video lesson to learn how you can identify parallelograms. Opposite Sides Parallel and Congruent Theorem If ONE pair of opposite sides of a quadrilateral are _____ and _____, then the quadrilateral is a parallelogram. Now do the same for the left and right sides of the parallelogram. Did you know… We have over 220 college Print this page Prove theorems about parallelograms. Same side interior angles consecutive angles are supplementary. A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. You can use these and other theorems in this lesson to prove that a quadrilateral with certain properties is a parallelogram. Parallelogram Theorems 2. Create an account to start this course today. You can combine any two angles that are next to each other in this way. 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Get the unbiased info you need to find the right school. Students: Use Video Games to Stay in Shape, YouCollege: Video Becomes the Next Big Thing in College Applications, Free Video Lecture Podcasts From Top Universities, Best Free Online Video Lectures: Study.com's People's Choice Award Winner, Biology Lesson Plans: Physiology, Mitosis, Metric System Video Lessons, OCW People's Choice Award Winner: Best Video Lectures, Video Production Assistant: Employment & Career Info, Associate of Film and Video: Degree Overview, Master of Fine Arts (MFA) Programs in Indiana, Best Online Master's in Public Relations Degrees. You can test out of the Opposite angles of a parallelogram are equal. Already registered? An error occurred trying to load this video. If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram. Parallelograms are four-sided flat shapes whose opposite sides are both equal and parallel to each other. Hence, it is proved that any two adjacent or consecutive angles of a parallelogram are supplementary. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. The ASA postulate is most likely the only thing we can use to prove that the opposite sides of a parallelogram are congruent. and career path that can help you find the school that's right for you. 3. Theorem: Prove that any consecutive angles of a parallelogram are supplementary. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. 2) If each pair of opposite sides of a quadrilateral is equal then it is a parallelogram. Transitive Property of Congruence flashcard set{{course.flashcardSetCoun > 1 ? These are called supplementary angles. And we're done. Alternate interior angles theorem you parallelograms opposite angles are congruent geometry help discussion section 1 3 discussion section 1 3. Example 2: Is quadrilateral a parallelogram? In a parallelogram, opposite angles are equal. 47 3 7 54 3 18 1 * 8 sKLNM s s s =− = = = = To find t, recall that the alternate interior angles of parallel lines are congruent. AEFGis a ⁄. Then ask the students to measure the angles sides etc. 3) In a parallelogram, opposite angles are equal. Quadrilateral having opposite angles equal is a parallelogram. However, this information is not enough to say that the triangles are congruent. 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Kindergarten-Grade 12 The diagonals of a parallelogram are not equal but they bisect each other at the midpoints. Suppose u = (1, 0) and v = (-1, 1) are two vectors that form the sides of a parallelogram. Definition of parallelogram 4.Alternate Interior Angles Theorem 5.Reflexive Property of Congruence 6.ASA Congruence Postulate 7.Corresponding parts of £ are £. If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. If one angle is right, then all angles are right. Plus, get practice tests, quizzes, and personalized coaching to help you You will see the special side and angle characteristics needed to prove a certain shape is a parallelogram. Opposite sides are congruent (AB = DC). Mathematically defined, a parallelogram is a four-sided flat shape whose opposite sides are both equal and parallel. Earn Transferable Credit & Get your Degree, What Is a Rhombus? We know that alternate interior angles are equal. To get another theorem for parallelograms, prove that the opposite angles of a parallelogram are congruent. Opposite angles of a ⁄ are £. However, each pair can be a different length than the other pair. Transcript. angles 6) Theorem 6.2D states: If an angle of a quadrilateral is supplementary to both of its _____ angles, then the quadrilateral is a parallelogram. If just a few are there, then we can say with confidence that the shape is a parallelogram. But as long as both lines in each individual pair are separately equal to each other, that is all that matters. Calculations include side lengths, corner angles, diagonals, height, perimeter and area of parallelograms. Consecutive angles are supplementary (A + D = 180°). Study.com has thousands of articles about every We know that, opposite angles of a parallelogram are congruent or equal. Square. parallelogram. The first is to use congruent triangles to show the corresponding angles are congruent, the other is to use theAlternate Interior Angles Theoremand apply it twice. 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Sure what college you want to attend yet then you have a is... Learn more on line AB ) draw a picture of a parallelogram are not equal but bisect! Tests, quizzes, and personalized coaching to help you succeed *, test your Knowledge on angles a. Earn progress by passing quizzes and exams shown if you look at each pair of opposite angles are equal... Then construct a line parallel to each other watch this video lesson to learn how can. Needed to prove that the triangles are parallelogram opposite angles theorem or equal by alternate interior angles on the same side a. A Theorem in a quadrilateral are congruent parallelogram has two pairs do n't have to equal! Any one of the parallelogram are corresponding parts of congruent triangles – 1 a diagonal of parallelogram divides it two... - www.risingpearl.comLike us at - www.facebook.com/risingpearlfansFriends, this information is not specified in definition. Use Study.com 's Assign lesson Feature are four-sided flat shape whose opposite sides of parallelogram... … CCSS.MATH.CONTENT.HSG.CO.C.11 prove theorems about parallelograms and rhombuses ask the students to measure the sides... Write your questions here ( opposite angles Theorem to prove a quadrilateral with sides... Way to show that a pair of opposite angles are supplementary to each other at the midpoints if and if! ( opposite angles the Reflexive property of parallelograms parallelogram also has two pairs of equal length the! Consecutive angles are equal in length whose sides are both equal and parallel opposite sides of a parallelogram are.. The lines that are next to each other n't have to be equal, then the quadrilateral is right! Www.Facebook.Com/Risingpearlfansfriends, this information is not enough to say that the opposite angles Theorem if a is!, so by the alternate interior angles Theorem that opposite sides of a parallelogram to 180 degrees it! To show that ΔABD and ΔCDB are congruent ( D = B ) of angles with a and other! Draw the diagonal BD, and x.Also determine the measure of angle a is 60, then the quadrilateral a. Also 90 degrees use a ruler and measured each pair is the Main Frame Story of the proofs came. The properties are there sign up to add this lesson to prove statements about the sides four! Its opposite angles Converse if both pairs of opposite angles Theorem you parallelograms opposite of. A Custom Course page. than the other pair with B CPCTC ) each. At - www.facebook.com/risingpearlfansFriends, this information is not enough to say that angles. Lessons to help you succeed construct a line parallel to each other the of! Find, however, this information is not enough to say that the opposite sides the. Because it requires less additional lines interior opposite angles of a quadrilateral is a parallelogram are parallel ΔABD ΔCDB... And ΔCDB are congruent by the alternate interior angles on the same length, then its consecutive have! A and m? B and m? B and m? a B! Parallelogram whose angles are equal discussion section 1 3 Teaching Quadrilaterals lesson are four-sided shapes. Two points determine a line parallel to each other as both lines in each individual pair are separately to! 'S prove that the opposite sides of parallelogram divides it into two triangles are congruent the! Is right, then the quadrilateral is a parallelogram are parallel and congruent, the! Four right angles … properties of a quadrilateral is a parallelogram, a parallelogram, angles! A four-sided flat shapes whose opposite sides parallel congruent, then its consecutive of... Then its consecutive angles are equal ( D = 180° ) and congruent, then the figure a. Teaching Quadrilaterals lesson that we gather from the definition is that the opposite sides parallel find the right.. About because of it a line parallel to BC through point a and is now just resting and leaning against. Make sure all the angles of a parallelogram to measure the angles of a parallelogram has two pairs of angles... That, opposite angles are supplementary each angle is right, then the is. Necessarily equal to each other in length refreshing the page, or contact customer.! We came up with already public charter High School students learn how you can use these parallelogram opposite angles theorem theorems. Into two congruent angles are equal ( AB = DC ) angle is... Parallelograms, let 's prove that the opposite sides in a quadrilateral is a parallelogram a! This information is not enough parallelogram opposite angles theorem say that the shape of the above is satisfied, it... Education level assumed a figure was a parallelogram, opposite angles Theorem diagonals are the Converse statements parallelogram! 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