Geometer's Sketchpad Lab

Quadrilateral Properties Due Date: Tuesday, Nov 11, 2014

1.Completethe steps to CONSTRUCT (not draw) each quadrilateral. That means, when you drag a vertex or resize, your quadrilateral must still fit the definition. Also construct the two diagonals as dotted segments and their intersection point in each quad.

2.Measure every distance and every angle. After you’ve headed and titled the document and all measures are taken, then print preview – fit to page –and print the construction. Move a point to change measures. (It must still fit the definition or you've found a problem with your construction steps.) Reprint. You now have two construction diagrams.

3.Create and print the script. On the sketch, select all. Go to the custom tool in the tool bar: . Choose “Create New Tool”.
(A) Name the new tool after the quadrilateral.
(B) Check “Show Script View.”
(C) Type your name in the comments line.
(D) Right click in white space to page set up and print.

NOTE: As an example of steps 2 and 3, the irregular quadrilateral has been completed for you. A copy is attached. Yes, all of your work should have a complete heading, titled with the name of the quadrilateral, and organized with subheadings like the example. This will also help you know what you did or didn’t measure.

4.Go to the grid on the last page of this lab report and check ALL the characteristics that ALWAYS apply to each quad. Your measurements must support your answers!

You will hand in (stapled in this order):

⎕Grid/table, completed – with your name and period written on it in the space provided – on the top.

⎕Kite, 2 sketches and 1 script

⎕Parallelogram, 2 sketches and the script

⎕Rectangle, 2 sketches and the script

⎕Rhombus, 2 sketches and the script

⎕Square, 2 sketches and the script

⎕Non-isosceles trapezoid, 2 sketches and the script

⎕Isosceles trapezoid, 2 sketches and the script

AMDG

Name______Ms. Kresovic

Course______, period ______Assigned R 22 Oct 14. Due T 11 Nov 14*

SUMMARY OF QUADRILATERALPROPERTIES

Directions:Place an X in each box IF that property is ALWAYS true for that quadrilateral. (Do not put an X in any box that is only sometimes true.) *This assignment MUST be handed in on time. If you are having difficulty, you must communicate with me BEFORE the due date for a possible extension (which will only be granted for extenuating circumstances). Note: This project takes me about two weeks to grade. Late papers will be penalized 10% per day it is late. This assignment is worth 100 points.

Important:Be sure your measures on pages 1-4 support your answers here. No guessing! You will lose points for each missing Xor extra X, so be sure to mark this grid carefully!

Irregular Quadrilateral / Kite
(that is not a rhombus) / Parallelogram / Rectangle
(that is not square) / Rhombus
(that is not square) / Square / Trapezoid / Isosceles
Trapezoid
  1. Has exactly four sides

  1. Exactly one pair of parallel opposite sides

  1. Two pairs of parallel opposite sides

  1. Exactly one pair of congruent opposite sides

  1. Two pairs of congruent opposite sides

  1. Exactly one pair of congruent opposite angles

  1. Two pairs of congruent opposite angles

  1. Congruent diagonals

  1. Perpendicular diagonals

  1. Each Diagonal bisectsthe other diagonal

  1. Only one Diagonal bisects the other diagonal

  1. Both diagonals bisect a pair of opposite angles

  1. One diagonal bisects a pair of opposite angles

  1. Four congruent angles (at the four vertices)

  1. Four congruent sides

  1. ALL pairs of consecutive angles are supplementary

  1. Some, but not all, pairs of consecutive angles are supplementary

  1. Four right angles (at the four vertices)

  1. Diagonals form four congruent right triangles

  1. Diagonals form four congruent isosceles right triangles


The following pages are for your reference only.

You do not need to complete them or hand them in.

Construction Steps / Construction 1 & Measures / Construction 2 & Measures
Irregular Quadrilateral
This is the only one that requires NOCONSTRUCTION steps since we do not need any congruent, parallel, or perpendicular sides. (Just draw any four unrelated points and connect them with segments, so this is NOT a construction.)
Hint: You may use arrows if some spots on your sketch get too crowded for measures. / /
Kite
By def: kite has 2 (disjoint) pairs ofcongruent consecutive sides
(disjoint pairs involve all 4 sides, can't use one side in both pairs.)
1. Make two intersecting circles with different radii.
2. Construct the intersection points of the two circles as two of the kite's vertices.
3. Use the centers of the circles as the other two radii.
Hint: No need to use up space on your lab sheet to show the rest of the circles since we really only needed them to create the two radii (equidistant points). / Drag your construction to look "similar” to this shape & write in all the measures. / Drag your construction to look "similar” to this shape & write in all the measures.
Parallelo-gram
By def: a has TWO pairs of | | opposite sides.

1. From a pt (1st vertex), make any 2 seqments to be the first two sides.
2. Select one of the segments and the non-adjacent endpoint and CONSTRUCT a parallel line.
3. Select the other segment and endpoint and CONSTRUCT another______line.
4.Construct the intersection point of the lines from
steps 2 & 3 as the
4th ______. / Drag your construction to look "similar” to this shape & write in all the measures. / Drag your construction to look "similar” to this shape & write in all the measures.
Rectangle
By def: rect. is a w/ ONE rt. angle, so do NOT use perp. construction at more than one corner!
1. Draw any segment as a 1st side
2. At ONE endpt, construct a perpendicular to the segment.
3.Select any point on one this segment to be a 3rd ______.
4.Through two vertices, construct a ______(answer is not perp!) to the opposite side to find the 4th vertex. / Use any non-square rectangular shape & write in all the measures here. / Drag a vertex to make a very different looking rectangle & write in all the measures here.
Rhombus
By def: rhombus is a w/ two congruent consecutive sides. Don't construct more than those conditions!
1. Draw any circle
2. Construct 2 radii to use as the 1st & 2nd sides of the rhombus
3.
4. / Drag your construction to look "similar” to this shape & write in all the measures. / Drag a vertex to make a very different looking rectangle & write in all the measures here.
SQUARE
By def: square is a rhombus and rectangle. Don't construct more than those conditions.
1. Draw any circle
2. Construct 1 radius to use as the 1st side of the square.
3.
4. / Use any square & write in all the measures here. / Rotate & change the size of your square & write in all the measures here.
(Non-isosceles) Trapezoid
By def: trap. has exactly one pair of | | opposite side. Don't construct more than those conditions. / Drag your construction to look "similar” to this shape & write in all the measures. / Drag your construction to look "similar” to this shape & write in all the measures.
Note: | | bases need not be "top" & "bottom"
Isosceles Trapezoid
By def: trap w/ congruent legs. Don't construct more than those conditions.
1. Draw a segment as a 1st side
2. Use one endpt as a center of a circle. Choose a good pt on the circle as the 3rd vertex.
3.Through the 3rd vertex, construct a parallel to the 1st side.
4.At the other endpt of the 1st side, construct a circle congruent to the previous circle.
5.Construct the intersection point of the parallel line with the 2ndcircle as the 4th vertex. / Drag your construction to look "similar” to this shape & write in all the measures. / Drag your construction to look "similar” to this shape & write in all the measures.