Mt 322 Topics in Geometry - Fall 2002
Department of Mathematics & Computer Science
CARDINAL STRITCH UNIVERSITY
Sr. Barbara E. Reynolds, Ph.D.
Study Guide for Test #1.5
Test date: Thursday, October 24
This test will cover major concepts in Chapters 1 - 4, and the article
from the Mathematics Teacher that was assigned. In particular,
you should be able to:
- do some basic geometric constructions,
- write step-by-step proofs of some geometric statements,
- give a counter-example (disproof) of a statement if it is not true in
- set up a truth table and evaluate a Boolean expression,
- use basic area, perimeter, and volume formulas of geometry,
- work with simple linear expressions and equations,
- use algebra and analytic as a tool in solving problems, and
- work with various one- and two-dimensional coordinate systems.
- Basic Geometric Constructions
You should be able to perform the following
- construct a perpendicular from point P to a line l using only the
circle and line tools (not the shortcuts on the GSP menubar),
- construct the perpendicular bisector of a given line segment,
- find the foot of the perpendicular from a point P to a line l,
- construct a tangent to a circle from a point P on the circle,
- construct a tangent to a circle from a point P exterior to the circle,
- construct the bisector of a given angle,
- define a rectangular, square, or polar coordinate system on a GSP worksheet,
- perform any of the above constructions on a coordinate grid as well
as on a GSP worksheet without the coordinate grid,
- define and plot a function in either Cartesian or polar form on a
GSP worksheet, and
- modify the domain of the function (by selecting the function -- only
the function, then choosing Properties, then Plot in
the Edit menu).
- Truth Tables and Boolean Expressions
The development of geometric proofs rests on the basic rules of logic.
You should be able to
- set up a truth table for Boolean expressions involving AND, OR, and
- evaluate a Boolean expression involving AND, OR, and NOT, (that is,
you should be able to determine whether the expression is true or
- set up a truth table for a Boolean expression involving an implication,
- identify the hypothesis and the conclusion of an implication
statement (a proposition or a theorem),
- negate a Boolean expression involving AND, OR, and NOT,
- negate a simple statement involving a universal or existential
quantifier. (This test will not include mutiple levels of quantifiers.)
- Basic Geometric Formulas
- You should know and be able to use basic area, perimeter, and volume formulas
- You should be able to use the Pythagorean theorem to find the lengths
of the sides of a right triangle.
- You should be able to apply these formulas to solve perimeter, area,
and volume problems for composite geometric figures constructed from
- You should be able to identify pairs of similar triangles (using AAA),
as well as pairs of congruent triangles.
- Basic Algebra
While this test will focus on the geometric ideas we have been
studying in Chapters 1 - 4, you should be able to work with simple
linear expressions and equations in solving problems. Since Chapter 4 is
on Analytic Geometry, problems involving more algebra than those in Test #1
are very likely! (See the
Benchmark Study Guide
for a more explicit list of basic algebra skills.)
- Developing a Proof
The test will include two or three opportunities to explain, prove,
and/or disprove a particular geometric statement or construction.
- You should be able to prove that your strategy for doing any of
the basic geometric constructions listed above is correct.
- You should be able to use the Pythagorean theorem in a proof
involving lengths and right angles.
- You should be able to use the idea that the angle in a semi-circle is
a right angle in a proof.
- You should be able to identify and use similar triangles in a proof.
- You should be able to identify whether two given triangles are (or
are not) congruent and/or similar.
- You should be able to prove or disprove that a given pair of
triangles is similar (or congruent). (What are the criteria that we can
use to prove that a pair of triangles is similar? ... congruent?)
- You should be able to use coordinates in developing a proof.
Return to Sr. Barbara E. Reynolds
for 2002 -- 2003.
Go to Mt 322 Topics in Geometry Syllabus.
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This page was updated on October 17, 2002.