# What shape are the diagonals are congruent?

## Brijesh Write up 3

Page history last edited by Brijesh Patel 11 years, 10 months ago

1. The shape you get when you Construct two segments of different length that are perpendicular bisectors of each other you get a figurethat can be discribed as a Rhombus and a paralellogram. (It isalso a quadralateral)

2. The shape you get when you repeat the same steps for number one but use congruent segments can be discribed as a square, rhombus, rectangle, and paralellogram. (It is also a quadralateral)

3. The figure formed below when two segments that are not perpendicular cross can be discribed as a paralellogram.

4. A figure that is formed with the same conditions as number three but with congruent segments can be discribed as asquare, rectangle, rhombus, and parallelogram. (It is also a quadralateral)

5. This extremely complicated shape to construct can be discribed as a kite.

6. I have constructed all shaped except for an isosceles trapezoid and a trapezoid. In an isosceles trapezoid the diagnals are congruent and the bases are paralell.

7.

ConditionQuadrilateralReasioningDiagonals are perpendicularSquare, Kite, RhombusAs you can see with the pictures above the diagonals for these three shapes cross at a 90 degree angle, becuase of this they are congruent.Diagonals are perpendicular but only one diagonal is bisectedSame shapes as above.Again these shape's diagonals bisect each other at a 90 degree angle making them congruent.Digonals are congruent and intersect but are not perpendicularRectangleAs you can see with the rectangle above it has two bisectors but these bisectors unlike the ones with the square, kite do not intercect at 90 degress.Diagonals bisect each otherSquare, Kite, Rhombus, Rectangle, paralellogram.As you can see in the pictures above all of those shapes are made with bisecting diagonals except for the concave quadrilateral.Diagonals are perpendicular and bisect each other.Same shapes from the first box.As you can see with the pictures above the places where the diagonals intersect are perpendicularDiagonals are congruent and bisect each otherSquare, rectangle, Trapezoid (Isosceles specifically)The diagonals (bisectors) are congruent for the these two shapes.Diagonals are congruent, perpendicular and bisect each other.SquareFor a square all the diagonals are congruent and all intersect at a 90 degree angle.

8. As you add more conditions to describe the diagonals, less diagonals can be diecribed as a result. For exaple if you have the condition "diagonals bisect each other" then you are talking about All of the shapes made above along with trapezoids, but with the exception of the concave quadrilateral. If you add the condition "Diagonals are congruent, perpendicular, and bisect each other then you have a square not all of those shapes. JUSTTHESQUARE.

9.

FigureNamesPropertiesaParalellogram/Rectangle

Opposite sides are parallel, Opposite sides are congruent, Opposite angles are congruent, Each diagonal forms two congruent triangles, Diagonals bisect each other,

Diagonals are congruent, All angles are right angles. Two pairs of consecutive sides are congruent.

bKiteOnly one pair of poosite angles is congruent, Diagonals are perpendicular, Diagonals bisect vertex anglescSquare, Rectangle, Rhombus, ParalellogramOpposite sides are parallel, Opposite sides are congruent, Oppositeangles are congruent., each diagonal forms 2 congruent trianlges, Diagonals bisect each other, Diagonals are congruent, All angles are right angles, Two pairs of consecutive sides are congruent.dIsosceles TrapezoidOnly one pair of oppsite sides is parallel. Only one pair of opposite sides is congruent, Diagonals are congruent, Two pairs of consective sides are congruent.eParalellogramOpposite sides are parallel, Opposite sides are congruent, Each digaonal forms 2 congruent triangles, Diagonals bisect each otherfRhombus, Kiteoppsite sides are parallel, Opposite sides are congruent, Opposite angles are congruent, Each diagonal forms 2 congruent triangles, Diagonals bisect each other,Diagonals are perpendicular. Diagonals bisect vertex angles, All sides are congruent

10.

PropertyParallelogramRectangleRhombusSquareIsos TrapezoidKiteoppsite sides are parallelxxxxOnly one pair of opposite sides is parallelxOpposite sides are congruentxxxxOpposite Only one pair of opposite sides is congruentxOpposite angles are congruentxxxxOnly one pair of opposite angles is congruentxEach diagonal forms 2 congruent trianglesxxxxDiagonals bisect each otherxxxxDiagonals are perpendicularxxxDiagonals are congruentxxxDiagonals bisect vertex anglesxxAll angles are right anglesxxAll sides are congruentxxTwo pairs of consecutive sides are congruentxxx

11. A. Parallelogram - For aquadrailateral tobe a parallelogram it must have: opposite sides areparallel, Opposite sides are congruent, Opposite angles are congruent, eachdiagonal forms 2 congruent triangles, and diagonals bisect each other.

B. Rectangle - For a quadrailateral to be a rectangle is must have: Opposite sides are parallel, Opposite sides are congruent, Opposite angles are congruent, Each diangnal forms 2 congruent triangles, Diagonals bisect each other, Diagonals are congruent, all angles are right angles, two pairs of consecutive sides are congruent.

C. Rhombus - For a quadrilateral to be a rhombus is must have: Opposite sides are parallel, Opposite sides are congruent, Opposite angles are congruent, Each diagonal forms 2 congruent triangles, Diagonals bisect each other, diagonals are perpendicular, Diagonals bisect vertex angles, All sides are congruent.

D. Square - For a quadrilateral to be a square is must have: Opposite sides are parallel, Opposite sides are congruent, Opposite angles are congruent, EAch diagonal forms 2 congruent triangles, Diagonals bisect each other, Diagonals are perpendicular, Diagonals are congruent, all angles are right angles, all sides are congruent, two paris of consecutive sides are congruent.

E. Kite - For a quadrilateral to be a kite it must have: Only one pair of opposite angles is congruent, Diagonals are perpendicular, and diagonals bisect vertex angles.

F. Isos trapezoid - For a quadrilateral to be a isos trapezoid is must have: only one pair of opposite sides parallel, Only one pair of opposiute sides is congruent, Diagonals are congruent, Two pairs of consecutive sides are congruent.