This Geometry unit is actually the compilation of the two separate Geometry units. Key components are;
Surface Area and Volume
Parallel Lines with Transversals & Proofs
Triangle Congruence & Proofs
Quadrilaterals and Parallelograms
There are several parts to each of these areas. This unit should take about 3 weeks to complete.
We begin this unit by reviewing the relationship of the angles formed by two parallel lines cut by a transversal. In summary, any two angles formed by these parallel lines cut by a transversal are either congruent or supplementary.
The types of angles formed are;
Vertical Angles Corresponding Angles Alternate Interior Angles Alternate Exterior Angles
Linear Pairs Consecutive Interior Angles Consecutive Exterior Angles
Each of these are the result of parallel lines cut by a transversal.
Other important vocabulary terms are;
Line Line Segment Supplementary Angles Complementary Angles Coplanar Points or Lines
Angle Bisector Segment Bisector Skew Lines Adjacent Angles Congruent
Triangles can be classified by either sides or angles.
Classification of triangles by sides;
Scalene Triangle - no sides have equal length
Isosceles Triangle - at least two sides are equal in length (congruent)
Equilateral Triangles - all sides are equal in length (congruent)
Classification of triangles by angles;
Acute Triangle - all angles have measures less than 90 degrees
Right Triangle - the triangle has exactly one 90 degree angle
Obtuse Triangle - the triangle has exactly one angle greater than 90 degrees but less than 180 degrees
Use these terms and your knowledge of them to complete the following homework assignment.
In this second section, we begin to look at proofs that are related to two parallel lines cut by a transversal and congruent triangles. Each of these concepts are often used to help prove the other. More often, the parallel lines cut by a transversal is used to help prove triangle congruence. In both cases, it is important to remember that in geometric proofs, steps and reasons must be given for every step in the proof.
The "note sheet" below has a list of possible reasons for these type proofs along with the 5 types of triangle congruence relationships that can be proved. These are the only 5 ways triangles can be proven congruent.
Each of the examples for this note sheet will be completed in class.
The solutions to the proofs on the note sheets are found below.
Now that we have a couple of examples and a little practice, try the following homework assignment.
The third section of this unit looks at the properties of parallelograms. The properties have to do with the relationships between sides, angles, and diagonals of parallelograms.
The following note sheet states these relationships, has a couple of parallelogram proofs (fill in the blank type), and a few exercises for practice.
Section 4.4 Quadrilaterals
In this section, we look at a few special types of parallelograms along with some other special quadrilaterals. The special parallelograms are;
Each of these have all the attributes of a parallelogram along with some characteristics that are unique to each of them. These are spelled out on the note sheet below.
The other quadrilaterals are;
The special characteristics are also given on the note sheet.
You should make sure to take note of the Trapezoid Midsegment Theorem. Not only what it says, but what it does.