Quadrilaterals
By: Valerie Jackson
Kite
Construction
- Create an angle of any sort (<BAC)
- Construct a circle with center A radius AB.
- Plot points B and C where the circle from #2 intersects the angle from #1.
- Construct a circle with center C and a random radius (radius CD.)
- Construct a circle with center B and radius CD.
- Connect points B and D to create line segment BD.
- Connect points C and D to create line segment CD.
A=(pq)/2
Where p and q are the diagonals
Angle relationships:
The angles between unequal sides are equal
Side relationships:
Two sets of congruent adjacent sides
Diagonal Relationships:
The diagonals intersect at right angles
Symmetries:
A kite has one line of symmetry that goes through the vertexes between congruent sides
Rectangle
Construction
- Draw line l and plot two random points (points A and B)
- Create a perpendicular line to line l that goes through point B
- Create another perpendicular line to line l that goes through point A
- Construct a circle with center A radius AC
- Construct a circle with center B radius AC
- Plot point D where the perpendicular line that goes through B intersects the circle from #5
- Connect points C and D to create the line segment CD.
wl=A
where w is width and l is length
Angle Relationships:
All angles are equal to each other and are equal to 90 degrees
Side Relationships:
Opposite sides are congruent and parallel
Diagonal Relationships:
Diagonals are congruent
Symmetries:
There are two lines of symmetry that both go through the middle of each side and extend to the opposite side.
Square
Construction:
- Create a random line segment (Line AB)
- Create a perpendicular bisector to line segment AB
- Name the bisector line CE
- Construct a circle with center C and radius CB
- Name the point where the circle and line CE intersect point D
- Construct a perpendicular bisector to line CE that goes through point D.
- Construct a circle with center D and radius CB and plot point F where the circle intersects with the line segment from #6
- Connect points F and B to create line segment FB
A=a^2
where a is equal to a side length
Angle Relationships:
All angles are equal to each other and are equal to 90 Degrees
Side Relationships:
All side are congruent to each other
Diagonal Relationships:
Diagonals are congruent
Symmetries:
There are four lines of symmetry, two of with are the diagonals and two that go through the midpoint of each line and extend to the midpoint of the opposite side.
Rhombus
Construction
- Create a line with two points (Line AB)
- Construct a circle with center A radius AB
- Create a random point on the circle (point C)
- Create a circle with center C radius AB
- Create a circle with center B radius AB
- Create a point where the circle from #4 and #5 intersect and name that point D
- Connect point A to point C to create line segment AC and connect point C to point D to create line segment CD and connect point D to point B to create line segment DB
A=(pq)/2
where p and q are the diagonals
Angle Relationships:
Opposite angles are equal
Side relationships:
All sides are equal in length and opposite sides are parallel
Diagonal Relationships:
The diagonals intersect at right angles
Symmetries:
There are two symmetries, that both extend through opposite points.
Parallelogram
Construction
- Create an angle of any sort (Angle CAB)
- Create a circle wit center A and a radius of anything (radius AZ)
- Create a circle with center B and radius AZ
- Plot point D where the circle from #3 intersects with line AB
- Create a circle with center D radius ZY
- Plot point E where the circle from #3 and #5 intersect
- Construct a circle with center B and radius AC
- Plot point F where the circle from #7 intersects the line BE
- Create line segment CF by connecting points C and F
A=bh
where b is base and h is height
Angle Relationships:
opposite angles are congruent and consecutive angle are supplementary
Side Relationships:
Opposite sides are parallel and congruent
Diagonal Relationships:
Each Diagonal cuts the other diagonal in half
Symmetries:
There are no lines of symmetry
Construction
- Create an angle of any sort (angle ABD)
- Construct a circle with center B radius BA
- Create a circle with center D radius BA
- Plot point E where the circle from #3 intersects the angle from #1
- Create a circle with center E and radius CA
- Plot point F where the circles from #3 and #5 intersect
- Create a parallel line to line BA that goes through points D and F
- Plot the two random points G and H on parallel lines and connect them to create in segment GH
A={(b1+b2)/2}h
where b1 and b2 are the bases and h is height
Angle relationships:
There are no specific angle relationships
Side relationships:
There is one pair of opposite parallel sides
Diagonal Relationships:
There is no diagonal relationships
Symmetries:
None
Isosceles Trapezoid
Construction:
8. Plot random point H on line BA
9. Construct a circle with radius BD and center H
10. Plot point G where the circle from # 9 intersects with the line DF
11. Connect points G and H to from line segment GH
A={(b1+b2)/2}h
where b1 and b2 are the bases and h is the height
Angle Relationships:
Angles that touch the same parallel side are equal
Side Relationships:
One set of Parallel sides, and the two sides that are not parallel are the same length
Diagonal Relationships:
Diagonals are congruent
Symmetries:
There is one line of symmetry that goes trough the mid point of the two bases