properties of trapezium,kite,parallelogram,rhombus,rectangle,square
Answers
Every trapezium shows the following properties:
1)Angle: The sum of angles in a trapezoid-like other quadrilateral is 360°. So in a trapezoid ABCD, ∠A+∠B+∠C+∠D = 360°.
2)Two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°.
3)Its diagonals bisect with each other.
4)The length of the mid-segment is equal to 1/2 the sum of the bases. In the above figure mid-segment= 1/2 (AB+CD)
5)In special cases of the isosceles trapezium, legs of the trapezium are congruent to each other. This means that despite being non-parallel, the measurement of both the legs is equal.
Kite:
Following are properties of a kite:
Two pairs of sides known as consecutive sides are equal in length.
One pair of diagonally opposite angles is equal in measurement. These angles are said to be congruent with each other.
The diagonals meet each other at 90°, this means that they form a perpendicular bisection
Parallelogram:
There are six important properties of parallelograms to know:
Opposite sides are congruent (AB = DC).
Opposite angels are congruent (D = B).
Consecutive angles are supplementary (A + D = 180°).
If one angle is right, then all angles are right.
The diagonals of a parallelogram bisect each other.
Each diagonal of a parallelogram separates it into two congruent triangles.
Rhombus:
All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary).
All sides are congruent by definition.
The diagonals bisect the angles.
The diagonals are perpendicular bisectors of each other.
Rectangle
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EducationMathGeometryProperties of Rhombuses, Rectangles, and Squares
Properties of Rhombuses, Rectangles, and Squares
RELATED BOOK
Geometry For Dummies, 2nd Edition
By Mark Ryan
The three special parallelograms — rhombus, rectangle, and square — are so-called because they’re special cases of the parallelogram. (In addition, the square is a special case or type of both the rectangle and the rhombus.)
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The three-level hierarchy you see with
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in the above quadrilateral family tree works just like
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A dog is a special type of a mammal, and a Dalmatian is a special type of a dog.
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Here are the properties of the rhombus, rectangle, and square. Note that because these three quadrilaterals are all parallelograms, their properties include the parallelogram properties.
The rhombus has the following properties:
All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary).
All sides are congruent by definition.
The diagonals bisect the angles.
The diagonals are perpendicular bisectors of each other.
The rectangle has the following properties:
All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).
All angles are right angles by definition.
The diagonals are congruent.
Square:
The square has the following properties:
All the properties of a rhombus apply (the ones that matter here are parallel sides, diagonals are perpendicular bisectors of each other, and diagonals bisect the angles).
All the properties of a rectangle apply (the only one that matters here is diagonals are congruent).
All sides are congruent by definition.
All angles are right angles by definition.