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all trapezoids are parallelograms

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Isosceles trapezoid

An isosceles trapezoid ( isosceles trapezium in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Some sources would qualify all this with the exception: "excluding rectangles." Two opposite sides (bases)

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Question:1. Which of the above quadrilateral's diagonals are congruent? 2. Which of the above quadrilateral's diagonals bisect each other? 3. Which of the above quadrilateral's diagonals are perpendicular? 4. Which of the above quadrilaterals are regular? 5. Which of the above quadrilateral's both pairs of opposite sides are parallel? 6. Which of the above quadrilateral's have exactly one pair of opposite sides that are parallel? 7. Which of the above quadrilateral's have both pairs of opposite sides are congruent? 8. Which of the above quadrilateral's each diagonal bisects two angles?

Answers:1. parallelogram, rectangle, rhombus, square, and isosceles trapezoid 2. parallelogram, rectangle, rhombus, square, and isosceles trapezoid 3. rhombus and square 4. parallelogram, rectangle, rhombus, square, trapezoid, and an isosceles trapezoid? 5. parallelogram, rectangle, rhombus, square 6. trapezoid, and isosceles trapezoid 7. parallelogram, rectangle, rhombus, square 8. all

Question:Is a quadrilateral a parallelogram? Is a rectangle a parallelogram? Is a square a trapezoid? Is a trapezoid a quadrilateral? They are part of my review for my final but I always get confused which are which..

Answers:Yes, all parallelograms are quadrilaterals. Yes, all rectangles are parallelograms. Yes, all squares are trapezoids. Yes, all trapezoids are quadrilaterals. (A trapezoid, is by definition, any quadrilateral with at least one pair of parallel sides). http://planetmath.org/encyclopedia/Trapezoid.html *From The Words of Mathematics by Steven Schwartzman (1994, Mathematical Association of America): trapezoid (noun); trapezoidal (adjective); trapezium, plural trapezia (noun): The Greek word trapeza "table" was composed of tetra "four" and the Indo-European root ped- "foot." A Greek table must have had four feet (= legs). The suffix -oid (q.v.) means "looking like," so that a trapezoid is a figure that looks like a table (at least in somebody's imagination). Some Americans define a trapezoid as a quadrilateral with at least one pair of parallel sides. Under that definition, a parallelogram is a special kind of trapezoid. For other Americans, however, a trapezoid is a quadrilateral with one and only one pair of parallel sides, in which case a parallelogram is not a trapezoid. The situation is further confused by the fact that in Europe a trapezoid is defined as a quadrilateral with no sides equal. Even more confusing is the existence of the similar word trapezium, which in American usage means "a quadrilateral with no sides equal," but which in European usage is a synonym of what Americans call a trapezoid. Apparently to cut down on the confusion, trapezium is not used in American textbooks. The trapeze used in a circus is also related, since a trapeze has or must once have had four "sides": two ropes, the bar at the bottom, and a support bar at the top. http://mathforum.org/dr.math/faq/formulas/faq.quad.html One last argument for the trapezoid being a quadrilateral with AT LEAST one pair of parallel sides: http://mathforum.org/library/drmath/view/54901.html

Question:State whether your trapezoid is isosceles.

Answers:I am not in a classroom, so I can't help with the "in your classroom" part. All these shapes are found in ordinary objects. You just have to look around - learn what each shape looks like, then look around or think what looks like that. For example, the monitor of a computer is a rectangle - so is a cell phone.

Question:rectangle trapezoid rhombus square 2) The diagonals must be congruent in which of the following? a rectangle a parallelogram a trapezoid none of these

Answers:1) A parallelogram is a 4 sided polygon where the opposite sides are equal. Trapezoids are the only shapes in the first list that don't satisfy the condition. Trapezoid 2) A rectangle is the only shape that satisfies the question. This is because all of the corners are at 90 degree angles and the opposite sides are congruent. Rectangle

From Youtube

6 1 Practice quiz solutions parallelogram and trapezoid comparison :Comparing the characteristics of trapezoids and parallelograms. Addressing the question as to whether a parallelogram is also a trapezoid. The answer will depend on your definition of trapezoid. If a trapezoid has exactly one pair of parallel lines, then parallelogram doesn't fit within those conditions or parameters. If your definition of trapezoid states that is has at least one pair of parallel sides, then all parallelograms could be considered trapezoids. Your answer then depends on your definition.

Parallelogram :Parallelogram Definition: A quadrilateral with two pairs of parallel sides. Squares, rectangles and rhombi are parallelograms ... Trapezoids and kites are not. The opposite sides of a parallelogram are congruent and the opposite angles of a parallelogram are congruent The consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. The diagonals of a rectangle are congruent, like those of an isosceles trapezoid. The diagonals of a rhombus are perpendicular, like those of a kite. See www.algebratunes.com