geometry-labs

4. No triangles; the sum of angles is greater
than 180°.
5. Exactly one triangle; SSS
6. Exactly one triangle; SAS
7. Exactly two triangles; SSA
8. Exactly one triangle;ASA
9. Exactly one triangle; SAA
10. No triangles; SSSA—too many constraints
Discussion Answers
A. See Notes and Answers above.
B. See Notes and Answers above. SSS, SAS, and
ASA are criteria for congruence of triangles.
So is SAA, which is essentially a version of
ASA, because once two angles are determined,
the third is too.
C. See Notes and Answers above.
D. Problem 7
Lab 6.2: Walking Parallelograms
This is an opportunity to review the angles
created when a transversal cuts two parallel lines,
while getting started on the general classification
of quadrilaterals. Students often are confused
about “Is a square a rectangle, or is a rectangle
a square”This lesson provides one way to get
some clarity on this or at least provides an
additional arena for discussion. See Lab 5.2
(Triangle and Quadrilateral Symmetry) for a
complementary approach.
Students could be paired up, with each member
of the pair executing the instructions written by
the other member.The values of the variables
must be stated before starting the walk.
In Problem 5, note that a variable should NOT
be used in the case of the angles of the square
and rectangle, since they are always 90°.
For Problems 9 and 10, you may give the hint
that there are five true statements of the type
“a rhombus is a parallelogram” that apply to
the four quadrilaterals discussed.
To summarize, you may explain how a tree
diagram or a Venn diagram can be used
to display the relationships between the
four figures.
Rhombi
Rhombi
Quadrilaterals
Parallelograms
Squares
Quadrilaterals
Parallelograms
Squares
Rectangles
Rectangles
Question F is a way to follow up on a discussion
about hierarchical relationships among
quadrilaterals, rather than a direct extension of
the lab.The answer to the question “Is a
parallelogram a trapezoid” depends on how a
trapezoid is defined.
Answers
1. The first two turns add to 180°, since you’re
facing opposite to your original position.
2. Turn right 40°;
Walk forward one step;
Turn right 140°;
Walk forward three steps;
Turn right 40°.
3. 40° and 140°
4. Do this twice:
Walk forward x steps;
Turn right a°;
Walk forward y steps;
Turn right (180 a)°.
200 Notes and Answers Geometry Labs
© 1999 Henri Picciotto, www.MathEducationPage.org