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WEEK 22 (assignment #8) – 20 points (due 2/23)
Parallelogram Constructions
Construct each of the following parallelograms starting with an angle.
Use three alphabetically sequenced letters on each angle to identify
its vertex, and one point on each side (at different distances from
the vertex). There are four angles to be used either
(a) Acute opening to the right
(b) Acute opening to the left
(c) Obtuse opening to the right or
(d) Obtuse opening to the left
For example you could use this angle for the starting point for
problem 2(b)
D
E
F
Each construction must be accompanied with a mathematical description
that matches the completed constructions. For example if you made an
angle congruent to another angle that were CA’s, you could write:
1  2, CA => AB ǁ CD
Construction Problems (using original angles a,b,c or d)
1 By definition, a parallelogram has two pairs of opposite
parallel sides:
(a,b) Use corresponding angles (CA) to make two pairs of
parallel sides
(c,d) Use Alternate Exterior Angles (AEA) to make two pairs of
parallel sides
2 (a,b)One pair of opposite sides are both parallel and congruent
(c,d)Both pairs of opposite sides are congruent
3 (a,b) Both adjacent angles are supplementary
(c,d) Diagonals bisect each other
Construction Problems (using original parts)
In these constructions, you have one or more original parts that must be copies into a new figure to make a special type of parallelogram (continue to
box in the mathematical descriptions that match your constructions that prove your shape is the special parallelogram)
(4) Using two original non-congruent sides, construct a rectangle (must make at least one right angle)
(5) Using an original diagonal construct a rectangle (must bisect the original diagonal, and use half its length for the radius of a circle)
(6) Using an original side, construct a Rhombus.
(7) Using an original side, and an angle, construct a Rhombus that has the angle as one of its vertices.
(8) Using two original non-congruent diagonals, construct a Rhombus. HOW? Copy one diagonal (d1), bisect it, and then on its perpendicular
bisector, make a circle with a radius half as long as the other original diagonal (d2)
(9) Using an original diagonal,, construct a square
(10) Using an original side, construct a square
(11) Using two original non-congruent sides, construct a Kite.
(12) Using four non-congruent sides, construct a Trapezoid.
(13) Using three original sides, construct an isosceles Trapezoid.