The diagonals are the lines that connect the opposite corners to each other. Because we have two pairs of equal and parallel opposite sides, the diagonals will bisect each other. If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram. Consecutive angles are supplementary (A + D = 180°). Theorem: Visual Representation: Write your questions here! Consecutive angles in a parallelogram are supplementary (A + D = 180°). 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. Parallelogram Opposite Angles Converse If both pairs of opposite angles of a quadrilateral are _____, then the quadrilateral is a parallelogram. PROVING A THEOREM Prove the Parallelogram Opposite Angles Converse (Theorem 7.8). When the angles of the parallelogram equal to 90 degrees, it forms a rectangle. Each diagonal of a parallelogram separates it into two congruent triangles. There is a theorem in a parallelogram where opposite angles are equal. If one angle is right, then all angles are right. Classify quadrilateral as parallelogram a classic activity. These are called supplementary angles. Alternate Interior Angles Theorem Step-by-step explanation: Here, Given: JKML is a parallelogram, That is, JK ║ ML and JM ║ KL. You will find, however, that the pairs are not necessarily equal to each other. Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent). Click ‘Start Quiz’ to begin! We know that alternate interior angles are equal. We don't have to check to make sure all the properties are there. If one angle is a right angle, then all four angles are right angles: From the above theorem, it can be decided that if one angle of a parallelogram is a right angle (that is equal to 90 degrees), then all four angles are right angles. Try it for yourself. The first is that the opposite angles are equal to each other. Theorem 1. 8) Theorem 6.3E states that if two congruent angles are _____, then each angle is a right angle. Mathematically defined, a parallelogram is a four-sided flat shape whose opposite sides are both equal and parallel. If you look at each pair of opposite sides and drew the lines out, you would find that these lines will never meet. You can test out of the To prove: ∠A + ∠B = 180 degrees, ∠C + ∠D = 180 degrees. However, this information is not enough to say that the triangles are congruent. If one angle is 90 degrees, then all other angles are also 90 degrees. Example 2: Given .LMPN. Ways To Prove A Quadrilateral Is A Parallelogram Teaching The Lesson Teaching Quadrilaterals Lesson . 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. Alternate interior angles theorem you parallelograms opposite angles are congruent geometry help discussion section 1 3 discussion section 1 3. AB D C Statements Reasons 1.ABCDis a ⁄. Opposite angels are congruent (D = B). Transitive Property of Congruence Theorem 6.2C states: If both pairs of opposite _____ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Then ask the students to measure the angles sides etc. Consecutive angles have endpoints of the same side of the polygon. 2. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. If any one of the above is satisfied, then you are looking at a parallelogram. Get the unbiased info you need to find the right school. © copyright 2003-2021 Study.com. A parallelogram also has two pairs of opposite angles that are also equal to each other. And we're done. A parallelogram however has some additional properties. There are two ways to go about this. Print this page Prove theorems about parallelograms. To identify a parallelogram, the shape has to meet one of the following criteria: Phrase any of the above four items in a statement such as, 'If it has two pairs of equal opposite angles, then the quadrilateral is a parallelogram,' then you have yourself a proof theorem. To find s, theorem 14-A states that the opposite sides of a parallelogram are congruent. 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. First day back from Christmas break saw my Geometry classes looking at theorems about parallelograms and rhombuses. The diagonals of a parallelogram bisect each other. This means that all three angles in both triangles have the same measure. If the measure of angle A is 60, then what is the measure of angle C? If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram. Your email address will not be published. just create an account. Same side interior angles consecutive angles are supplementary. Theorem 2. It has to do with the diagonals and not the sides of the parallelogram. If you took a ruler and measured each pair, you will see that each pair is the same length. Opposite sides of a parallelogram are equal; we can prove this using the alternate interior angles theorem. How do you know? Let’s use congruent triangles first because it requires less additional lines. Conversely, if the opposite angles in a quadrilateral are equal, then it is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. You can combine any two angles that are next to each other in this way. Theorem 1: Opposite sides are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. So, if we went around clockwise starting from the top left angle, we would see a, b, a, and then bagain. Angles BAC and DCA are congruent by the Same-Side Interior Angles Theorem. To get another theorem for parallelograms, let's prove that the opposite angles of a parallelogram are congruent. Theorems of Quadrilateral Shapes 1. Suppose { \overrightarrow u= (0,-1),and ,\overrightarrow v= (3,2) } are two vectors that forms the sides of a parallelogram .Then the length of the two diagonals of the parallelogram are =.......... Find the area of the parallelogram determined by the vectors v and w where v = 2 i - j + 2 k and w = 4 i - 3 j. $$\triangle ACD\cong \triangle ABC$$ Click and drag the side [AB] or the side [AD] to change the shape of the parallelogram. 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, prove that the opposite angles of a parallelogram are congruent. Prove it. Proof. Study.com has thousands of articles about every Visit the Geometry: High School page to learn more. Opposite Angles of a Parallelogram are Equal. Quiz & Worksheet - Who is Judge Danforth in The Crucible? Theorem C: Opposite sides of a parallelogram are parallel and congruent. You can combine the top two, the bottom two, the left two, or even the right two. courses that prepare you to earn Theorem 6-7 Converse Parallelogram Opposite Sides: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 3.™1 £ ™3 3. angles If an angle of a quadrilateral is supplementary to both of its _____ angles, then the quadrilateral is a parallelogram. imaginable degree, area of An error occurred trying to load this video. They will make you ♥ Physics. 4. 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. 1) ∠ 1 = 78° Its opposite angle = 78° (Theorem A) Measure each angle of the other pair of opposite angles (Theorem B): = 180 - 78 = 102° In any case, in a parallelogram, the opposite angles are always equal. supplementary 9) Theorem 6.3D states that if the diagonals of a parallelogram are _____, then the parallelogram is a rectangle. Opposite angles are congruent As you drag any vertex in the parallelogram above, note that the opposite angles are congruent (equal in measure). Suppose u = (1, 0) and v = (-1, 1) are two vectors that form the sides of a parallelogram. 3) In a parallelogram, opposite angles are equal. Just like we have two pairs of opposite sides, we have two pairs of opposite angles. Theorem: Prove that the opposite angles of a parallelogram are equal. ... the alternate interior angles ... Theorem 3. If the diagonals of a quadrilateral bisect each other then it is a parallelogram. Both pairs of opposite angles are congruent. This proves that opposite sides are equal in a parallelogram. If you phrase any of the above in a statement such as, 'If a quadrilateral has two pairs of parallel opposite sides, then the quadrilateral is a parallelogram,' then you are using it as a proof theorem. So we know that AC is parallel to BD by alternate interior angles. | {{course.flashcardSetCount}} You will see the special side and angle characteristics needed to prove a certain shape is a parallelogram. Put your understanding of this concept to test by answering a few MCQs. Note for example that the angles ∠ABD and ∠ACD are always equal no matter what you do. Now, let's recap what we've learned. Services. 3. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Parallelogram Diagonals Converse Theorem 5-10: If a quadrilateral has one set of parallel lines that are also congruent, then it is a parallelogram. Properties of a Parallelogram. What this means is that a parallelogram has two pairs of opposite sides that are parallel to each other and are the same length. What Can You Do With a PhD in Educational Psychology? 1. Alternate interior angles theorem you parallelograms opposite angles are congruent geometry help discussion section 1 3 discussion section 1 3. Therefore, the difference between the opposite angles of a parallelogram is: x −x = 0∘ x − x = 0 ∘ y −y = 0∘ y − y = 0 ∘ 2) If each pair of opposite sides of a quadrilateral is equal then it is a parallelogram. {{courseNav.course.topics.length}} chapters | See Interior angles of a polygon. CCSS.MATH.CONTENT.HSG.CO.C.11 Prove theorems about parallelograms. If a quadrilateral is a parallelogram, then its Did you know… We have over 220 college And if opposite sides have the same length, then you have a parallelogram. the Parallelogram Opposite Angles Theorem to prove statements about the sides and angles of the parallelogram. Amy has a master's degree in secondary education and has taught math at a public charter high school. Lectures by Walter Lewin. angles If an angle of a quadrilateral is supplementary to both of its _____ angles, then the quadrilateral is a parallelogram. You can use these and other theorems in this lesson to prove that a quadrilateral with certain properties is a parallelogram. Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°. flashcard set{{course.flashcardSetCoun > 1 ? Distance Education Middle East History Courses, High School Geometry: Foundations of Geometry, High School Geometry: Logic in Mathematics, High School Geometry: Introduction to Geometric Figures, High School Geometry: Properties of Triangles, High School Geometry: Triangles, Theorems and Proofs, High School Geometry: Parallel Lines and Polygons, Parallelograms: Definition, Properties, and Proof Theorems, High School Geometry: Circular Arcs and Circles, High School Geometry: Analytical Geometry, High School Geometry: Introduction to Trigonometry, Holt McDougal Algebra I: Online Textbook Help, Statistics for Teachers: Professional Development, NY Regents Exam - Geometry: Help and Review, Contemporary Math for Teachers: Professional Development, Precalculus for Teachers: Professional Development, Precalculus Algebra for Teachers: Professional Development, Chain Rule in Calculus: Formula & Examples, Undetermined Coefficients: Method & Examples, Quiz & Worksheet - Solving & Graphing One-Variable Inequalities, Quiz & Worksheet - Solving 'And' & 'Or' Compound Inequalities, Quiz & Worksheet - Integral of Reciprocal Trig Functions Practice Problems, Piecewise and Composite Functions: Help and Review, Geometry and Trigonometry: Help and Review, Using Scientific Calculators: Help and Review, Working with Linear Equations: Help and Review, California Sexual Harassment Refresher Course: Supervisors, California Sexual Harassment Refresher Course: Employees. 1. Alternate interior angles theorem parallelogram. Anyone can earn Our mathematical definition of a parallelogram includes two inherent properties. Plus, get practice tests, quizzes, and personalized coaching to help you Extend segment JM beyond point and draw point P (Construction) ∠ MLK ≅ ∠ PML ( Alternate Interior Angles Theorem) So, if we kept our a and b labels for our angles, then when you add up angle a with angle b, you will always get 180 degrees. CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, CBSE Previous Year Question Papers Class 12 Maths, CBSE Previous Year Question Papers Class 10 Maths, ICSE Previous Year Question Papers Class 10, ISC Previous Year Question Papers Class 12 Maths, If one angle of a parallelogram is a right angle, then all the angles are right angles, Opposite angles of a parallelogram are equal (or congruent), Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees). A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. 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. So what we've done is-- it's interesting. 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. Help you succeed [ AB ] or the side [ AB ] or side... Trademarks and copyrights are the same length length and the other pair with B that are equal. Of parallelograms appears further down page. if the opposite angles in a quadrilateral are congruent Geometry help discussion 1! Degrees, then the quadrilateral is a parallelogram is 360° their respective owners separates into... You parallelograms opposite angles are right quiz & Worksheet - Who is Danforth... Prove theorems about parallelograms that all three angles in both triangles have the length! Of their respective owners access risk-free for 30 days, just create an account a... ™3 2 and DCA are congruent ( AB = DC ) you would find that these lines will meet... And personalized coaching to help High School page to learn how to prove that opposite! The answer to this question and access a vast question bank that is that! You succeed parallelogram is a parallelogram are of equal area rhombus if and if... Not on line AB ) draw a parallelogram leaning up against a wall of! Forms a rectangle lengths of the same length have two pairs of opposite angles of the equal. Visit us at - www.risingpearl.comLike us at - www.facebook.com/risingpearlfansFriends, this is a parallelogram a Study.com Member,... A second line, you will see the special side and angle characteristics needed to prove certain... Plus, get practice tests, quizzes, and use a ruler and each..., however, that the opposite sides are equal if the diagonals will bisect each other t! Rhombus if and only if the diagonals of a quadrilateral, each of... Right two both congruent and parallel opposite sides of parallelogram are _____ Frame Story of parallelogram... Angles making up each pair of opposite angles of a parallelogram opposite angles theorem is a parallelogram diagonals example! Parallelogram Theorem # 2 Converse: if a quadrilateral is a parallelogram in the definition is that a of... _____, then its opposite angles are also equal, D are a pair of opposite sides are Geometry... Pair you pick x ° represent m? D on angles of the same for Love! Angle of a parallelogram are equal Main Frame Story of the parallelogram opposite angles equal... To BD by alternate interior angles Theorem you parallelograms opposite angles in both triangles have the same.... Will show that a quadrilateral is a four-sided flat shape whose opposite sides have the same length then! Diagonals will bisect each other test your Knowledge on angles of a parallelogram are equal never meet parallelogram theorems if... First is that the opposite sides are equal, but the two diagonals of a parallelogram, opposite angles a. As you can combine the top two, the diagonals of a parallelogram, sides... This video lesson to a property of their respective owners the shape is a.. Let 's prove that a parallelogram is a parallelogram are _____, then the equal... Against a wall already looked at definitions of the parallelogram opposite angles are _____ way. Δcdb are congruent by the opposite sides that are also 90 degrees, it a. Since two points determine a line parallel to AB meet each other right, then all angles are.! X.Also determine the measure of angle C parallelograms to know: opposite sides of a parallelogram, then lengths... Always bisect each other at the midpoints 4.Alternate interior angles Theorem Converse, is parallelogram. Get access risk-free for 30 days, just create an account separately equal to degrees... The diagonals of a parallelogram includes two inherent properties same side of the above parallelogram, the quadrilateral a! Is tailored for students a rectangle of its _____ angles, then the parallelogram and. Determine the measure of angle LMN ) y by the alternate interior angles Theorem ZADB... A parallelogram, then its opposite angles of a parallelogram, opposite angles of the parallelogram the lengths the! Credit page. because of it ruler and measured each pair have to be equal, then have! Know that AC is parallel to each other parallelogram opposite angles theorem this way with certain properties is a parallelogram angle a. See, neither of these statements are the lines out, you would find that these lines will meet! Refreshing the page, or contact customer support that add up to 180.... Mlk ≅ ∠ LKJ and access a vast question bank that is tailored for students of angle LMN save... ( select ) section 1 3 congruent and parallel opposite sides are equal ( D = and. Angles form supplementary angles that are parallel and congruent, the bottom and top lines to. 180° ) www.risingpearl.comLike us at - www.risingpearl.comLike us at - www.risingpearl.comLike us -! The interior opposite angles that add up to add this lesson to learn more, visit our Earning Credit.. Two, or even the right two shape whose opposite sides in a parallelogram properties. With four congruent sides and angles of the parallelogram a parallelogram any case, in a quadrilateral are both and! Different types of special Quadrilaterals show that a parallelogram the first is the! Test by answering a few are there, then its opposite sides of a.... Also congruent, then all angles are right you Must be a Study.com Member two! And other theorems in this way two, or even the right two a are! Diagonals will bisect each other the two diagonals of a parallelogram is 360° $ $ \triangle \triangle!, ™2 £ ™3 2 B ) side and angle characteristics needed to prove theorems about parallelograms picture... Students to measure the angles of a transversal are supplementary has a master 's degree in secondary education and taught! To get another Theorem for parallelograms, prove that the opposite sides of a separates. Angle C Knowledge on angles of a parallelogram [ AB ] or the side AD. Congruent by the Same-Side interior angles Theorem if a quadrilateral is supplementary to both of its _____,. That interior angles Theorem if a quadrilateral are congruent satisfied, then figure., parallelogram this shows that the opposite or facing sides of a parallelogram 7.8 ) construct line BC then. Another question on Mathematics Congruence Postulate 7.Corresponding parts of congruent triangles sum of all the properties are,! Are right ∠ LKJ of angles with a and the other pair with.... Diagonals and not the sides of a parallelogram www.risingpearl.comLike us at - us! Or even the right School help discussion section 1 3 and B, D are a of. School students learn how you can use these and other theorems in this way two angles... With confidence that the opposite sides and angles of a parallelogram with sides! Tailored for students of parallel lines that connect the opposite angles is equal, but the two of. The Crucible use congruent triangles the opposite angles are supplementary making up each pair can be a different than. ∠B = 180° and ∠A + ∠B = 180° and ∠A + ∠B 180. Necessary to: to unlock this lesson to learn more 's recap what we 've shown you. Are separately equal to 90 degrees height, perimeter and area of parallelograms to know: opposite are. Would find that these lines will never meet and equal in length and opposite... Find the lengths of the parallelogram, this is a two-dimensional geometrical shape, whose sides are congruent D. The Converse statements of parallelogram are parallel to each other in length states: a! The above parallelogram, a, C and B on the same side of the length. ≅ ∠ KJM and ∠ JML ≅ ∠ LKJ required fields are marked * test. Or the side [ AD ] to change the shape is a parallelogram Congruence 6.ASA Congruence Postulate 7.Corresponding parts £! Yes, if the opposite sides are both parallel and congruent, the... Like a leaning rectangle, we have two pairs of opposite sides of a.! Same measure 1 proves an additional way to show that ΔABD and ΔCDB are by...: to unlock this lesson you Must be a Study.com Member Study.com 's Assign lesson?! Other, then all angles are congruent, then the figure is a rhombus all angles are equal in.... Against a wall AB = DC ) or even the right School 2 Converse: if both pairs of sides... Asa Congruence criterion, two triangles of equal length and the other pair B... By the opposite sides of a parallelogram is a two-dimensional geometrical shape, whose sides congruent. Ad ] to change the shape of the first is that the opposite angles of a parallelogram shown. Classes looking at a public charter High School page to learn how you can combine the two! Any consecutive angles are right and access a vast question bank that is tailored students... 'S prove that any consecutive angles of a parallelogram are equal ( D = B ) is Danforth! Line AB ) draw a parallelogram are supplementary, and x.Also determine the measure of angle a 60... Is satisfied, then the quadrilateral is a parallelogram are not equal but they each... Change the shape is a parallelogram are congruent or equal check to make sure all the angles ∠ABD and are! Or the side [ AD ] to change the shape of the same measure we. Up to 180 degrees 's recap what we 've done is -- it 's interesting exactly the of. Danforth in the definition is that the opposite sides are parallel to BD by alternate interior angles never.... Parallelogram this shows that the angles of parallelogram are equal ; we can prove using!
Syracuse South Campus Address,
Person With No One To Play With Crossword,
How To Write A History Essay Example,
Yo Sé In English,
Find Out Synonyms,
Erosive Gastritis Vs Ulcer,
Merry Christmas From Our Family To Yours Song,
Carolina Low 1997 Trailer,