Geometer's Sketchpad Lab 5
Quadrilateral Properties
NAME_______________________________ _____/50
Due Date: Monday, Nov 9
1. Write brief steps to CONSTRUCT 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 quadrilateral.
2. Measure every distance and every angle. Make a sketch of your quad in the middle column here, writing in each measure
directly on the diagram as shown in the example.
3. Drag a vertex or resize the quadrilateral so it is clearly a different shape than in column 2. (It must still fit the definition or
you've found a problem with your construction steps.) Now make of sketch of this new quad in column 3 and write in all the
measures.
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!
Construction Steps
IRREGULAR
QUADRILATERAL
Sketch 1 & Measures
57.3
24.6
D
This is the only one that
3.1
requires
1.30
A
NO CONSTRUCTION
98.1 81.9
57.7
steps since we do not need
81.9
2.64
G
any congruent, parallel,
98.1
or perpendicular sides.
4.00
(Just draw any four
3.41
unrelated points and
connect them with
40.7
segments, so this is NOT a
46.6
construction.)
Hint: You may use arrows
if some spots on your sketch
get too crowded for
measures.
KITE
Sketch 2 & Measures
80.7
13.3
A
4.31
4.30
71.1
17.4
35.2
3.44
C
5.85
D 91.4
1.48
3.841
129.9
1.82
50.1
50.1
129.9G
2.38
38.5
32.6
4.25
58.9
B
B
36.8
4.92
6.06
17.5
Drag your construction to look "similar to
these shapes & write in measures.
By def: kite has 2 (disjoint)
pairs of congruent
consecutive sides
(disjoint pairs involve all 4
sides, can't use one side in
both pairs.)
F
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).
C
A
G
B
D
C
Construction Steps
Sketch 1 & Measures
Sketch 2 & Measures
PARALLELOGRAM
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.
C
D
2. Select one of the
segments and the nonadjacent 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 ______________.
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.
A
B
Construction Steps
Sketch 1 & Measures
Sketch 2 & Measures
RHOMBUS
By def: rhombus is a
w/
two congruent consecutive
sides. Don't construct
more than those
conditions!
D
F
1. Draw any circle
2. Construct 2 radii to
use as the 1st & 2nd
sides of the rhombus
3.
A
4.
B
SQUARE
By def: square is a rhombus
and rectangle. Don't
construct more than those
conditions.
1. Draw any circle
2. Construct 1 radii to
use as the 1st side of
the square.
3.
4.
E
Construction Steps
Sketch 1 & Measures
Sketch 2 & Measures
Note: | | bases need not be "top" & "bottom"
(NON-ISOSCELES)
TRAPEZOID
By def: trap. has exactly one
pair of | | opposite side.
Don't construct more than
those conditions.
ISOSCELES
TRAPEZOID
A
By def: trap w/ congruent
legs. Don't construct more
than those conditions.
E
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 2nd circle as the 4th
vertex.
F
B
SUMMARY OF PROPERTIES OF QUADRILATERALS
Directions: Place an X in each box IF that property is ALWAYS true for that quadrilateral. (Do not put an X if it is
only sometimes true.)
Important: Be sure your measures on pages 1-4 support your answers here. No guessing! You will lose points for each
1. Has exactly four sides
2. Exactly one pair of parallel opposite
sides
3. Two pairs of parallel opposite sides
4. Exactly one pair of congruent
opposite sides
5. Two pairs of congruent opposite
sides
6. Exactly one pair of congruent
opposite angles
7. Two pairs of congruent opposite
angles
8. Congruent diagonals
9. Perpendicular diagonals
10. Each Diagonal bisects the other
diagonal
11. Only one Diagonal bisects the other
diagonal
12. Both diagonals bisect a pair of
opposite angles
13. One diagonal bisects a pair of
opposite angles
14. Four congruent angles (at the four
vertices)
15. Four congruent sides
16. ALL pairs of consecutive angles are
supplementary
17. Some, but not all, pairs of
consecutive angles are
18. Four
right angles (at the four
supplementary
vertices)
19. Diagonals form four congruent right
triangles
20. Diagonals form four congruent
isosceles right triangles
Isosceles
Trapezoid
Trapezoid
Square
(not square)
Rhombus
(not square)
Rectangle
Parallelogram
(not a ombus)
Kite
Irregular
Quadrilateral
missing or extra X, so be sure to mark this grid carefully!