CARDINAL STRITCH UNIVERSITY

Sr. Barbara E. Reynolds, Ph.D.

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 general,
- 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 constructions:

- 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 NOT,
- evaluate a Boolean expression involving AND, OR, and NOT, (that is,
you should be able to determine whether the expression is
*true*or*false*), - 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 of geometry.
- 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 simpler figures.
- 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 Home Page.

Return to course list for 2002 -- 2003.

Go to Mt 322 Topics in Geometry Syllabus.

Return to Mt 322 Topics in Geometry Assignments.

The easiest way to contact me is to send an email message to Sr. Barbara E. Reynolds.

This page was updated on October 17, 2002.