The following proof demonstrates: So, we have proven that the opposite angles of a parallelogram are congruent. Yes, they are.1151, This angle and this angle--are they congruent? The parallelogram will have the same area as the rectangle you created that is b × h "0097, The second one: "If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. How To Prove a Quadrilateral is a Parallelogram (Step By Step) Using Coordinate Geometry to Prove that a Quadrilateral is a Parallelogram. The converses of the 1 3 Prove the parallelogram law: The sum of the squares of the lengths of both diagonals of a parallelogram equals the sum of the squares of the lengths of all four sides. To Prove: Quadrilateral ABCD is a parallelogram. Consider the following illustration. "0113, As long as we have (just like the property we learned in the previous lesson) a parallelogram, then we know that both pairs of opposite angles are congruent.0122, In the same way, the converse would be, "If both pairs of opposite angles are congruent, then it is a parallelogram. Isosceles trapezoid For which quadrilateral are the diagonals are congruent but do not bisect each other? There are also theorems on diagonals, and opposite sides of a quadrilateral. Sign up for our science newsletter! Practice: Prove parallelogram properties. Adobe, Apple, Sibelius, Wordpress and other corporate brand names and logos are registered trademarks of their respective owners. … Get immediate access to our entire library. 2 4. The Organic Chemistry Tutor 267,230 views Fill in the blank in the statement with always, sometimes or never. Solution ... ^2, \end{align} which is what we sought to prove. "0986, So, if you have to prove parallelograms, you can just use any one of these five--whichever one you can use, depending on what you are given.0997, Then, you can do that to prove parallelograms.1006, Let's actually go through some examples now: the first one: Let's determine if each quadrilateral is a parallelogram.1012, In this case, the first one, I have one pair of opposite sides being parallel, and I have the other pair of sides being congruent.1022, Now, if you remember, from the theorems and the definition of parallelogram that we went over, none of them say that this is a parallelogram.1034, So, if I see that one pair of opposite sides is parallel, and the other side is congruent, that is not a parallelogram.1045, This could be a parallelogram, but there is no theorem, and there is no definition, that says this.1056, The closest one...well, there are a few; one of them says that it has to be both pairs of opposite sides being parallel.1063, We have one pair being parallel; if these two sides were parallel, then we could use the definition of parallelogram.1073, If both pairs of opposite sides are congruent...we have one pair that is congruent; this pair is not congruent, so then we can't use that.1079, And then, the last one, the special one that we went over--that has to be the same pair.1089, So, one pair, the same pair of opposite sides, being both parallel and congruent--then it is a parallelogram.1095, So, if these sides are both parallel and congruent, then we have a parallelogram.1104, Or these sides--if they were both parallel and congruent, then we can use that one; but it is none of those.1111, So, this one is "no"; we cannot determine it.1121, It could be a parallelogram, but we can't prove it, because there is no theorem--nothing to use to state as a reason, so this is a "no. ... Rhombus, parallelogram, rectangle, square, and trapezoid. Oh, you thought they were over and done with, did you? Both congruent and parallel. The formula for the volume of a parallelepiped is the same as the formula for the area of a 2-D parallelogram. This is to save you time. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Related topics. Statements of parallelogram and its theorems 1) In a parallelogram, opposite sides are equal. Adding and simplifying. A rhombus is a special kind of parallelogram in which all four sides are equal length. "Given"--it was given to me.2258, Then, my next step: I am going to say...2277, Now, the angles that are in red--that is not the given statement; it is not anything that is given, so I have to state it and list it out.2281, I am going to say, "Angle AED" (I can't say angle E, because see how angle E can be any one of these;2291, so I have to say angle AED) "is congruent to angle CEB"; what is the reason for that?--"vertical angles are congruent. To do this, we will use the definition of a parallelogram or the following conditions. --one pair being both parallel and congruent?2040, We have that this pair is parallel; can we say that this pair is also congruent?2049, Well, because I can say that this angle is congruent to this angle...2056, let me do that in red; that way, you know that that is not the given...2067, since I know that these lines are parallel, if this acts as my transversal, I can say that this angle is congruent to this angle.2072, Remember: it is just line, line, transversal; angle, angle; do you see that?2091, This is B; this is D; this is this angle right here; and this is this angle right here.2104, I can say that those angles are congruent, because the lines are parallel.2114, Well, I can now prove that these two triangles are congruent, because of Side-Angle-Angle, or Angle-Angle-Side.2120, Therefore, the triangles are congruent; and then, these sides will be congruent, because of CPCTC.2130, And then, I can say that it is parallelogram, because of that theorem of one pair being both parallel and congruent.2140, Let me just explain that again, one more time.2149, I need to prove that this is a parallelogram with the information that is given to me.2152, All I have that is given is that this side and this side are parallel, and this and this are congruent.2157, From what is given to me, I can say that these angles are congruent, because they are vertical;2167, and I can say that these angles are congruent, because alternate interior angles are congruent when the lines are parallel.2174, The whole point of me doing all of this is to show this using a theorem that says, if one pair of opposite sides2182, are both parallel and congruent, then it is a parallelogram.2194, I want to show that this side is both parallel (which is given) and congruent, so that I can say that this whole thing is a parallelogram.2200, But the only way to show that this side is congruent is to prove that this triangle and this triangle are congruent,2209, so that these sides of the triangle will be congruent, based on CPCTC.2223, If you are still a little confused--you are still a little lost--then just follow my steps of my proof.2231, And then, hopefully, you will be able to see, step-by-step, what we are trying to do.2236, Step 1: my statements and my reasons (just right here): #1: the statement is the given,2241, AD is parallel to BC, and AE is congruent to CE; what is my reason? Introduction to Proving Parallelograms There are five ways to prove that a quadrilateral is a parallelogram: Prove that both pairs of opposite sides are congruent. Quadrilateral ABCD is a parallelogram; Parallelograms theorem. Well, we hate to burst your bubble, bud, but we learned about those triangles for a reason. © 2020 Science Trends LLC. Step Reason Statement BD Bisects AC ZOBE ZADE 1 Given 2 BC AD Select A Reason. "1790, No, quadrilateral ABCD is not a parallelogram, because opposite sides are not congruent.1801, If it was congruent, if they were the same, then you would have to go ahead and find the distance of BC,1818, find the distance of AD, and then compare those two.1823, For the last example, we are going to complete a proof of showing that it is a parallelogram.1829, Always look at your given; using your given, you are going to go from point A1840, (this is your point A; this is your starting point, and then this is your ending point; that is point B) to point B.1844, Right here, we know that AD is parallel to BC; oh, that is written incorrectly, so let's fix that; AD is parallel to BC; they were both wrong.1855, AD is parallel to BC, and AE is congruent to CE.1888, We know that those are true, and then we are going to prove that this whole thing is a parallelogram.1897, In order to prove that this is a parallelogram, we have to think back to one of those theorems1906, and see which one we can use to prove that this is a parallelogram.1913, The first one that we can use is the definition of parallelogram.1917, If we can say that both pairs of opposite sides are parallel, then it is a parallelogram.1921, All we have is one pair; we don't know that this pair is parallel, or can we somehow say that it is parallel?1928, I don't think so; the only way that we can prove that these two are parallel is if we have an angle,1937, some kind of special angle relationship with transversals--like if I say that alternate interior angles are congruent,1946, same-side/consecutive interior angles are supplementary...if I say that corresponding angles are congruent...1957, if something, then the lines are parallel; I could do that.1964, For this one, it would be alternate interior angles--if they were congruent,1969, if it somehow gave me that, then I could say that these two lines are parallel, AB and DC.1973, And then, I could say that the whole thing is a parallelogram, because I have proved that it has two pairs of opposite sides being parallel.1980, But I can't do that, because I don't have that information.1989, Can I say that both pairs of opposite sides are congruent, from what is given to me? Find missing values of a given parallelogram. A parallelepiped consists of 6 equal parallelogram faces. Unlimited access to our entire library. MP6. This definition includes various kinds of shapes. Prove a quadrilateral is a parallelogram using the converses of the theorems from the previous section. 3) Diagonals are perpendicular, 4) Opposite angles are congruent. The slope of AB is 3.0670, For BC, I am going to count from B to C; so I am going to count up/down first, the rise; do that one first.0683, From B to C, I have to go down; I am going to go 1, 2, 3, 4; I have to go down 4; so the slope of BC is -40692, (because going down is negative)...then from here, I am going to go 1, 2, 3, 4.0704, So, I went to the right 4, and that is a positive, because I went to the right, which makes this slope -1.0710, From C to D (it doesn't matter if you go from D to C or C to D), if I want to go from C to D,0720, then I am going to count 1, 2, 3, down 3; so the slope of CD is down 3, which is -3, over...0726, from here, I am going to go left 1; left 1 is -1; so then, -3/-1 is 3.0737, And then, from D to A, I can go...the slope of AD is 1, 2, 3, 4; that is a positive 4, because I am going up 4;0749, then 1, 2, 3, 4...that is a negative 4; I am going to the left 4.0764, And that makes this a negative 1; so since AB and CD have the same slope, I know that AB is parallel to CD.0770, And BC and AD have the same slope; that means that they are also parallel.0794, So, BC is also parallel to AD; I have two pairs of opposite sides parallel.0802, So, by the definition of parallelogram, this is a parallelogram, so yes, quadrilateral ABCD is a parallelogram.0813, OK, let's just summarize over the different theorems that we can use to prove parallelograms, before we actually start our examples.0843, A quadrilateral is a parallelogram if any one of these is true.0856, You don't have to prove all of these; just prove one of them.0863, If you prove one of these, then you can prove that the quadrilateral is a parallelogram.0867, The first one: a quadrilateral is a parallelogram if both pairs of opposite sides are parallel.0873, That is the definition of parallelogram; so as long as you can prove (this is the definition of parallelogram)--0882, as long as you can show--that this side is parallel to this side, and this side is parallel to this side,0892, then by the definition of parallelogram, the quadrilateral is a parallelogram.0902, The second one: If both pairs of opposite sides are congruent...as long as you show0909, that this side is congruent to that side and this side is congruent to that side, then you can state that this is a parallelogram.0916, Both pairs of opposite angles are congruent: that means that this angle is congruent to this angle, and this angle is congruent to this angle.0925, And remember: it has to be two pairs of opposite angles being congruent.0937, Diagonals bisect each other--not "diagonals are congruent," but "they bisect each other. 3. Drawing a line perpendicular from the base to one of the terminal points of the side gives you a right triangle with one of the sides equal to the height. The key to this proof (and probably most proofs about quadrilaterals) is a theorem about triangles. A segment bisector intersects line segment to make two congruent segments. In other words, a parallelogram is a 4-sided figure in which opposite pairs of sides lie parallel to each other. a rectangle), this formula simplifies down into the Pythagorean theorem a2 + b2 = c2. Simply multiply the area of the base by the height to find the volume. As with many 2-D shapes, a parallelogram has a corresponding analog in 3 dimensions. A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. Angle-Angle-Side.2446, If you are unsure what this is, then go back to the section on proving triangles congruent.2451, And then, we just proved that these two triangles are congruent by Angle-Angle-Side--that reason.2459, And then, now that the triangles are congruent, we can say that any corresponding parts of the two triangles are congruent.2467, Now I can say that AD is congruent to CB, and the reason is CPCTC; and that is "Corresponding Parts of Congruent Triangles are Congruent. Given: WXYZ is a parallelogram, ZX ≅ WY Prove: WXYZ is a rectangle What is the missing reason in Step 7? What is the perimeter of parallelogram LMNO? "2379, Now, I am just writing it out for those of you that don't have the name for it.2390, If you do, then you can just go ahead and write that out, and that would just be "alternate interior angles theorem. Look for and make use of structure. Proof 2 Here’s another proof — with a pair of parallelograms. A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. "1218, All right, the next one: Find the value of x and y to ensure that each is a parallelogram.1225, ABCD: now, we have to be able to find the value of x and y so that these two sides will be congruent, and then these two sides will be congruent.1233, If I want these two sides to be congruent, and find a number for y that will make these congruent, then I have to solve them being congruent.1246, 5y is equal to y + 24; here, I am going to subtract the y; so that way, this will be 4y is equal to 24.1257, Then, I divide the 4 from each side, and y is equal to 6.1273, If y is 6, then this will be 30; if y is 6, then this will be 30; so then, that is the value for y.1280, And then, for x, again, I have to do the same thing: so, 2x + 3 is equal to 3x - 4.1289, I am going to subtract the 2x here; you can add the 4 to this, so 7 is equal to x.1299, If x is 7, then this will be 14; this will be 17; here, this is 21 - 4, is 17.1317, The next one: now, this looks like it would be a square or rectangle, but you can't assume that.1329, I don't have anything that tells me that these are right angles; I don't have anything that tells me anything, really.1338, I have to find x and y so that these diagonals will be bisected, because that is what I am working with.1346, Then, this and this have to be congruent; this and this have to be congruent.1353, I am going to make x + 1 equal to 2x - 3, and then subtract the x here; 1 = x - 3; add the 3; then, this is 4 = x.1361, Let's see, the y's: this y and then this...this one is y + 4 = 20 - 3y.1388, So, if I add 3y, this is 4y + 4 = 20; subtract the 4; 4y = 16; divide the 4, and y = 4.1405, So then, now, if x is 4, and y is 4, then these parts of the diagonals will be congruent.1426, Therefore, the diagonals bisect each other, and then as a result, this is a parallelogram.1437, The next example: Determine if the quadrilateral ABCD is a parallelogram.1446, We are given the coordinates of all of the vertices of the quadrilateral.1453, And then, we have to determine if it is a parallelogram.1460, I can just draw it out here; it doesn't matter how you draw it, as long as, remember, when we label this out,1467, it has to be ABCD, or vertices have to be next to each other; it can't be jumping over, so it can't be ACDB--none of that.1475, It has to be in the order, consecutive.1488, And I am drawing this just to show which coordinates are next to each other, which ones are consecutive.1493, Again, you can use slope, or you can use the distance formula.1502, Since we used slope last time, let's use the distance formula this time.1506, I am going to find the distance of AB, compare that to the distance of CD, and see if they are congruent.1510, And then, before you move on, why don't you just try those two and see if they are congruent,1518, because if they are not, then you don't have to do any more work; you can just automatically say, "No, it is not a parallelogram. From this very simple definition of a parallelogram as a quadrilateral being composed of opposite pairs of parallel lines, we can deduce a key set of properties that all parallelograms must have by geometric necessity. Want to know more? Related topics. We're sorry to hear that! Question: Given: BD Bisects AC And ZCBEZADE. 2) Opposite sides are parallel. Identifying and Verifying Parallelograms Given a parallelogram, you can use the Parallelogram Opposite Sides Theorem (Theorem 7.3) and the Parallelogram Opposite Angles Theorem (Theorem 7.4) to prove statements about the sides and angles of the parallelogram. "1143, Now, this angle and this angle--are they congruent? Classify Quadrilateral as parallelogram A classic activity: have the students construct a quadrilateral and its midpoints, then create an inscribed quadrilateral. Extra Example 2: Use the Law of Cosines to Find the Missing Measure, Extra Example 4: Find the Measure of Each Diagonal of the Parallelogram, Example: Find the Circumference of the Circle, Extra Example 1: Use the Circle to Answer the Following, Extra Example 3: Given the Circumference, Find the Perimeter of the Triangle, Extra Example 4: Find the Circumference of Each Circle, Extra Example 1: Minor Arc, Major Arc, and Semicircle, Extra Example 2: Measure and Length of Arc, Theorem 2: When a Diameter is Perpendicular to a Chord, Extra Example 1: Central Angle, Inscribed Angle, and Intercepted Arc, Extra Example 1: Tangents & Circumscribed Polygons, Extra Example 2: Tangents & Circumscribed Polygons, Extra Example 3: Tangents & Circumscribed Polygons, Extra Example 4: Tangents & Circumscribed Polygons, Extra Example 1: Secants, Tangents, & Angle Measures, Extra Example 2: Secants, Tangents, & Angle Measures, Extra Example 3: Secants, Tangents, & Angle Measures, Extra Example 4: Secants, Tangents, & Angle Measures, Extra Example 1: Special Segments in a Circle, Extra Example 2: Special Segments in a Circle, Extra Example 3: Special Segments in a Circle, Extra Example 4: Special Segments in a Circle, Extra Example 1: Determine the Coordinates of the Center and the Radius, Extra Example 2: Write an Equation Based on the Given Information, Extra Example 4: Write the Equation of Each Circle, Extra Example 3: Exterior Angle Sum Theorem, Extra Example 4: Interior Angle Sum Theorem, Extra Example 1:Find the Area of the Shaded Area, Extra Example 2: Find the Height and Area of the Parallelogram, Extra Example 3: Find the Area of the Parallelogram Given Coordinates and Vertices, Extra Example 4: Find the Area of the Figure, Extra Example 1: Find the Area of the Polygon, Extra Example 2: Find the Area of the Figure, Extra Example 3: Find the Area of the Figure, Extra Example 4: Find the Height of the Trapezoid, Extra Example 1: Find the Area of the Regular Polygon, Extra Example 2: Find the Area of the Regular Polygon, Extra Example 3: Find the Area of the Shaded Region, Extra Example 4: Find the Area of the Shaded Region, Example: Scale Factor & Perimeter of Similar Figures, Example:Scale Factor & Area of Similar Figures, Extra Example 2: Find the Ratios of the Perimeter and Area of the Similar Figures, Extra Example 4: Use the Given Area to Find AB, Extra Example 4: Area of a Sector of a Circle, Extra Example 1: Name the Edges, Faces, and Vertices of the Polyhedron, Extra Example 2: Determine if the Figure is a Polyhedron and Explain Why, Extra Example 3: Describe the Slice Resulting from the Cut, Extra Example 4: Describe the Shape of the Intersection, Extra Example 1: Find the Lateral Area and Surface Are of the Prism, Extra Example 2: Find the Lateral Area of the Prism, Extra Example 3: Find the Surface Area of the Prism, Extra Example 4: Find the Lateral Area and Surface Area of the Cylinder, Lateral Area and Surface Area of a Right Cone, Lateral Area and Surface Are of a Right Cone, Extra Example 2: Find the Lateral Area of the Regular Pyramid, Extra Example 3: Find the Surface Area of the Pyramid, Extra Example 4: Find the Lateral Area and Surface Area of the Cone, Extra Example 1: Find the Volume of the Prism, Extra Example 2: Find the Volume of the Cylinder, Extra Example 3: Find the Volume of the Prism, Extra Example 4: Find the Volume of the Solid, Extra Example 1: Find the Volume of the Pyramid, Extra Example 2: Find the Volume of the Solid, Extra Example 3: Find the Volume of the Pyramid, Extra Example 4: Find the Volume of the Octahedron, Extra Example 1: Determine Whether Each Statement is True or False, Extra Example 2: Find the Surface Area of the Sphere, Extra Example 3: Find the Volume of the Sphere with a Diameter of 20 Meters, Extra Example 4: Find the Surface Area and Volume of the Solid, Extra Example 1: Determine if Each Pair of Solids is Similar, Congruent, or Neither, Extra Example 2: Determine if Each Statement is True or False, Extra Example 3: Find the Scale Factor and the Ratio of the Surface Areas and Volume, Extra Example 4: Find the Volume of the Larger Prism, Extra Example 1: Describe the Transformation that Occurred in the Mappings, Extra Example 2: Determine if the Transformation is an Isometry, Extra Example 1: Draw the Image over the Line of Reflection and the Point of Reflection, Extra Example 2: Determine Lines and Point of Symmetry, Extra Example 3: Graph the Reflection of the Polygon, Extra Example 2: Image, Preimage, and Translation, Extra Example 3: Find the Translation Image Using a Composite of Reflections, Extra Example 4: Find the Value of Each Variable in the Translation, Composite of Two Successive Reflections over Two Intersecting Lines, Angle of Rotation: Angle Formed by Intersecting Lines, Extra Example 2: Rotations and Coordinate Plane, Extra Example 3: Find the Value of Each Variable in the Rotation, Extra Example 4: Draw the Polygon Rotated 90 Degree Clockwise about P, Extra Example 2: Find the Measure of the Dilation Image, Extra Example 3: Find the Coordinates of the Image with Scale Factor and the Origin as the Center of Dilation, Extra Example 4: Graphing Polygon, Dilation, and Scale Factor, This is a quick preview of the lesson. © 2021 Educator, Inc. All Rights Reserved. *These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer. Q.E.D. Show that a quadrilateral is a parallelogram in the coordinate plane. You can transpose this triangle from the left side to the right side to make a normal rectangle. This geometry video tutorial provides a basic introduction into two column proofs with parallelograms. So, So, Hence, we see that the opposite angles in a parallelogram are equal. A square is a quadrilateral whose sides have equal length and whose interior angles measure #90^@#.. From the definition, it follows that a square is a rectangle. There are 5 distinct ways to know that a quadrilateral is a paralleogram. 3) In a parallelogram… "0134, It is just basically saying that if the opposite angles are congruent, then it is a parallelogram.0162, So, as long as we can prove this or this, then we can prove that it is a parallelogram.0180, Now, we have other options, too; there are actually more theorems.0186, The third theorem that we can use to prove quadrilaterals parallelograms is on their diagonals.0191, If we can prove that the diagonals (you can just say "if diagonals") bisect each other, then it is a parallelogram.0202, You can shorten it in that way; if you can just prove that the diagonals bisect each other,0223, in that way, then you have proven that the quadrilateral is a parallelogram.0235, And the fourth one, the last one: "If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. This geometry video tutorial provides a basic introduction into two column proofs with parallelograms. We help hundreds of thousands of people every month learn about the world we live in and the latest scientific breakthroughs. Welcome back to Educator.com.0000 For this lesson, we are going to use the theorems and the properties you learned in the previous lesson to prove parallelograms.0002 Turning the properties that we learned into actual theorems, if/then statements:0012 the first one: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.0020 Proofs of general theorems. Question 1172971: he reasons to the statements given. 2) If each pair of opposite sides of a quadrilateral is equal then it is a parallelogram. For this lesson, we are going to use the theorems and the properties you learned in the previous lesson to prove parallelograms. A. x = 11, y = 14 Consider parallelogram ABCD with a diagonal line AC. Prove the parallelogram law: The sum of the squares of the lengths of both diagonals of a parallelogram equals the sum of the squares of the lengths of all four sides. Question 1172971: he reasons to the statements given. Use the right triangle to turn the parallelogram into a rectangle. Determine whether the following statement is true or false. Opposite angels are congruent (D = B). There are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). Parallelograms can be used to represent the addition of vector components. "2515, Remember: this is point A and point B; this is the starting point and ending point.2539, So, see how I have this statement right here, and my last statement.2543, All we did was prove that these two sides are congruent, so that we could use the theorem that we just went over.2551, That is it for this lesson; thank you for watching Educator.com.2560. The first person to prove this fact about forces was Isaac Newton in his Principia Mathematica. I point out to students that for either of those pairs of triangles, I … Show that a quadrilateral is a parallelogram in the coordinate plane. Q.E.D. Similarly, drawing another transversal between points B and D would prove that the other two angles are equal. B E A D The resultant vector would look like this: Notice anything familiar about this shape? 22 cm C. 40 cm D. 80 cm. Write several two-column proofs (step-by-step). In fact, a rectangle is a quadrilateral whose interior angles measure #90^@#.This is one of the two conditions expressed above for a quadrilateral to be a square … No.1994, Can I say that opposite angles are congruent? The first person to prove this fact about forces was Isaac Newton in his Principia Mathematica. No.2002, I could say that these angles are congruent; they are vertical.2009, Or I could say that this angle and this angle are congruent, because they are vertical; but that is all I have with the angles.2013, Can I say that diagonals bisect each other?2020, Well, I have one diagonal that is bisected.2024, Can I somehow say that this diagonal is bisected?2027, I don't think so, just by being given parallel, congruent, and these angles--no.2034, Can I say that the last one works (remember the special theorem?) Proof: In Δ ABE and ΔCDE 1. We can prove this simply from the definition of a parallelogram as a quadrilateral with 2 pairs of parallel sides. One property of a parallelogram is that its opposite sides are equal in length. That's great to hear! Practice questions with step-by-step solutions. It is a quadrilateral where both pairs of opposite sides are parallel. For parallelograms, the adjacent angles are supplementary to each other (add up to 180°). *Ask questions and get answers from the community and our teachers! Ask lesson questions and our educators will answer it. Since this a property of any parallelogram, it is also true of any special parallelogram like a rectangle, a square, or a rhombus,. sum of squares of sides is equal to sum of squares of diagonals. line, alternate interior angles are congruent, ASA; two triangles sharing congruent angle, side, angle are congruent triangles. The two force vectors should combine into a new third vector that is a combination of the two. (Proof): Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other.