We've been studying properties of diagonals in various quadrilaterals (squares, rectangles, parallelograms, trapezoids, rhombuses, and kites).
What would you say is the connection in regards to the sides and angles of the quadrilaterals in relation to it's diagonal properties? (perpendicular or intersecting; congruent or non-congruent)
Draw, think, conjecture & justify!!!
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Squares-
SIDES & ANGLES= Perpendicular & Congruent
DIAGONALS= Pependicular & Congruent
Relation= Same
Rectangles-
SIDES= Perpendicular & Non-Congruent
ANGLES= Perpendicular & Congruent
DIAGONALS= Intersecting & Congruent
Relation- Same~ As & Ds Congruent Different~ Ss are Non-Congruent, Ss&As are Perpendicular, Ds are intersecting
Parallelograms-
SIDES & ANGLES= Intersecting & Non-Congruent
DIAGONALS= Intersecting & Non-Congruent
Relation= Same
Trapezoids-
SIDES & ANGLES= Intersecting & Non-Congruent
DIAGONALS= Intersecting & Congruent
Relation= Same~ Intersecting
Different~ Ss & As Non-Congruent, Ds~ Congruent
Rhombus-
SIDES & ANGLES= Intersecting & Congruent
DIAGONALS= Perpendicular & Congruent
RELATION- Same~ Congruent
Different~ Ss & As Intersecting, Ds Perpendicular
Kites-
SIDES & ANGLES= Intersecting & Non-Congruent
DIAGONALS- Perpendicular & Non-Congruent
RELATION- Same~ Non-Congruent
Different~ Ss & As Intersecting, Ds Perpendicular
- The number of sides equals the number of angles. You do n - 3 x n divided by 2.
- rectangles are mostly conruent
- rhombuses are mostly not congruent
- parallelagrams are mostly not congruent
- squares are mostly congruent
My congecture is that you take the number of sides subtract three from the number of sides then multiply your answere by the number of sides and divided it by half of the answere you got from the multiplcation problem. So all quadrelateals have two diagnals and a regular quarilaterals angles equal 90d. A squares diagnals are perpendicular, a rectangles diagnals are intersecting, a parrelograms diagnals are perpindicular, a trapoziods diagnals are intersecting, a rhumbases diagnals are intersectng and a kites diagnals are perpendicular.
square- P and C
rec.- I and C
Par.- I and C
rhombus- I and C
kite- P and NC
right trapezoid- I and NC
regular trapezoid- I and NC
What would you say is the
connection in regards to the sides and angles of the quadrilaterals in relation to it's diagonal properties? (perpendicular or intersecting; congruent or non-congruent)
Parallelogram- Opposite sides parallel and equal, opposite angles equal also. Diagonals only bisect each other. Not congruent.
Rectangle- Opposite sides parallel and equal and all right angles. Diagonals are equal.All Congruent.
Square- all sides are equal/perpendicular.All right angles.Diagonals are equal. All Congruent.
Rhombus- all sides equal, also opposite angles equal. Diagonals are perpendicular. Not congruent.
Trapezoid- One pair of opposite sides parallel.Diagonals congruent/legs congruent/base angles congruent.
~ B@NDFR3@K~
I will bring my drawings in tomorrow.
I will also bring my conjecture points, and proof.
all quadrilaterals have diagonals.
but the diagonals in the quadrilaterals sometimes are not congruent.
well.....
kites diagonals are not congruent.
squares diagonals are always congruent.
rectangles diagnles are always congruent.
parrellegrams are sometimes congruent but not always congruent.
rhombuses diagonals are congruent al the time.
We shall consider the following special types of quadrilaterals:
Square, Rectangle, Parallelogram, Rhombus, Kite, Trapezium.
First, there is more than one quadrilateral where the diagonals bisect each other. The square, rhombus, and kite have at least one or more bisecting diagonals. The square and rhombus have two bisecting diagonals, and the kite only one.
1. Diagonals are perpendicular when all sides of a quadrilateral are of equal length. Because the kite also has one bisecting diagonal, we must also state that diagonals can be perpendicular when two pairs of equal adjacent sides are present.
2. The diagonals of all quadrilaterals intersect.
3. A diagonal of any parallelogram forms two congruent triangles.
4. Both pairs of opposite sides of a parallelogram are congruent.
5. Both pairs of opposite angles of a parallelogram are congruent.
6. The diagonals of any parallelogram bisect each other.
There are 4 sides and 4 angles in a quadrilateral. If all 4 of the sides are conruent or opposite, then that will give you parallel and or congruant diagonals.
$ A square has all congruent sides and angles.
$ It has P and C diagonals.
* A regualr trapezoid has opp congruent sides and angles.
* It laso has parallel and congruent diagonals.
Module #3 Task #3
What would you say is the connection in regards to the sides and angles of the quadrilaterals in relation to its' diagonal properties? (perpendicular or intersecting; congruent or non-congruent)
We shall consider the following special types of quadrilaterals:
Square, Rectangle, Parallelogram, Rhombus, Kite, Trapezium.
First, there is more than one quadrilateral where the diagonals bisect each other. The square, rhombus, and kite have at least one or more bisecting diagonals. The square and rhombus have two bisecting diagonals, and the kite only one.
1. Diagonals are perpendicular when all sides of a quadrilateral are of equal length. Because the kite also has one bisecting diagonal, we must also state that diagonals can be perpendicular when two pairs of equal adjacent sides are present.
2. The diagonals of all quadrilaterals intersect.
3. A diagonal of any parallelogram forms two congruent triangles.
4. Both pairs of opposite sides of a parallelogram are congruent.
5. Both pairs of opposite angles of a parallelogram are congruent.
6. The diagonals of any parallelogram bisect each other.
A quadrilateral has equal diagonals somtimes, they are not congruent.
square=congruent
rectangle=congruent
parallelogram=somtimes
Whe you slit a quadrilateral in half you gaet two triangles, which equal 180 degrees. when you add that together you get 360 degrees which is the sum of a quadrilateral.
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