If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is_____a parallelogram Always To prove a quadrilateral is a parallelogram, it is ________enough to show that one pair of opposite sides is parallel That is true. Triangles can be used to prove this rule about the opposite sides. Get help fast. These geometric figures are part of the family of parallelograms: For such simple shapes, parallelograms have some interesting properties. Get better grades with tutoring from top-rated private tutors. Learn faster with a math tutor. 0 Why are these two lines not congruent (and other ways to figure out if other shapes are not congruent) Yes. (By definition). A parallelogram is a flat shape with four straight, connected sides so that opposite sides are congruent and parallel. 60 seconds . A parallelogram is a quadrilateral that has opposite sides that are parallel. That segment DG and segment EF are parallel as well as congruent. Its four interior angles add to 360° and any two adjacent angles are supplementary, meaning they add to 180°. A) The opposite sides of the parallelogram are congruent. Expand Image Take a rectangle and push either its left or ride side so it leans over; you have a parallelogram. D) The opposite angles of the parallelogram are congruent. Try to move the vertices A, B, and D and observe how the figure changes. The four line segments making up the parallelogram are WX, XY, YZ, and ZW. Theorem 1: Opposite Sides of a Parallelogram Are Equal In a parallelogram, the opposite sides are equal. Go with B. Mathematics. 60 seconds . Things that you need to keep in mind when you prove that opposite sides of a parallelogram are congruent. The figure is a parallelogram. You can examine them based on their diagonals, their sides or their interior angles. To show these two triangles are congruent we’ll use the fact that this is a parallelogram, and as a result, the two opposite sides are parallel, and the diagonal acts as a transv… Is it possible to prove a quadrilateral a parallelogram with two consecutive and two opposite congruent sides? A parallelogram is defined to be a quadrilateral with 2 pairs of opposite sides parallel. 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. Therefore,segment AB ≅ segment CD and segment BC ≅ AD because corresponding parts of congruent triangles are also congruent. The figure shows a side view of the li … ft. FGKL, GHJK, and FHJL are parallelograms. Solve for x. Opposite sides are congruent. Which statement can be used to prove that a given parallelogram is a rectangle? (10 Parallelograms have opposite interior angles that are congruent, and the diagonals of a parallelogram bisect each other. B) The diagonals of the parallelogram are congruent. Observe that at any time, the opposite sides are parallel and equal. If one angle is right, then all angles are right. Line segments XY and ZW are also congruent. Parallelogram definition A quadrilateral with both pairs of opposite sides parallel. Get better grades with tutoring from top-rated professional tutors. A tip from Math Bits says, if we can show that one set of opposite sides are both parallel and congruent, which in turn indicates that the polygon is a parallelogram, this will save time when working a proof.. Opposite (non-adjacent) angles are congruent. The opposite sides of a parallelogram are congruent so we will need two pairs of congruent segments: Now if we imagine leaving $\overline{AB}$ fixed and ''pushing down'' on side $\overline{CD}$ so that these two sides become closer while side $\overline{AD}$ and $\overline{BC}$ rotate clockwise we get a new parallelogram: Use the tools GeoGebra within this applet to investigate the answers to the following questions: 1) Are opposite sides of a parallelogram congruent? A parallelogram also has the following properties: Opposite angles are congruent; Opposite sides are congruent; Adjacent angles are supplementary; The diagonals bisect each other. The first rhombus above is a square while the second one has angles of 60 and 120 degrees. 62% average accuracy. Now, let's prove that if a quadrilateral has opposite sides congruent, then its diagonals divide the quadrilateral into congruent triangles. 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