Geometry A

This is a rigorous approach to plane geometry, emphasizing the logical

structure of geometry, proofs and critical thinking. All the concepts

mentioned in 6246 will be covered at great length. Excellence in the

quality of work is expected. Algebraic aspects of coordinate geometry

are included.

Geometry B

Throughout this course, sets of definitions and properties are used to

investigate geometric figures. Algebraic competency is expected. In

addition, the ability to apply arithmetic and algebraic skills to geometric

problems will be emphasized. A strong focus on deductive reasoning and

formal proof is also included.

Geometry C

A course for students who wish to become familiar with some geometric

concepts and their applications. The topics to be covered are reflections,

transformations, construction (ruler and compass), congruence and

application of congruence. This course emphasizes the numerical

relationships in geometric figures - angle measures, segment measures,

the Pythagorean theorem, area, volume and right triangle trigonometry.

Some logic and direct reasoning will be covered.

Enduring Understandings

 

Name, identify, classify, and sketch geometric figures.

Use protractor, ruler, and Sketch Pad to construct geometric figures.

Identify and solve measurement problems.

Identify and apply algebraic properties.

Identify and write valid conditional statements.

Solve algebraic problems.

Solve proportion problems.

Prove triangles similar and congruent

Prove lines parallel using theorems and postulates.

Solve application of the Pythagorean Theorem

Develop quadrilateral hierarchy.

Classify polygons.

Identify properties and apply formulas for polygons.

Find area and circumference of a circle.

Classify, find surface area, and find volume of 3-D figures.

Identify various linear formulas.

Find slope, midpoint, and distance between two points.

Perform transformations.

Find geometric probability. (A only)

Find matrix inverse. (A only)

Perform scalar and matrix multiplication. (A only)

Apply triangle properties.

Apply critical and logical thinking skills to proofs.

Identitfy types of angles.

Prove angle properties.

 

Essential Questions

What are the fundamental Geometric terms?

What angles are formed when two or more lines intersect?

Can you recognize Algebraic Properties?

What are deductive and inductive reasoning?

What are the types of triangles?

How do we know that two polygons are similar?

When would you use the Pythagorean Theorem?

What are the types, properties, and relationships among quadrilaterals?

What are they types, relationships, and properties of regular polygons?

What are the properties and relationships among circles?

Can you describe how to find the perimeter and area of geometric figures?

Can you describe how to find surface area and volume of 3-D shapes?

How does one apply Algebra to Geometry?

How do you describe basic transformations?

How do you analyze data?

Essential Vocabulary

Point	Line	Ray	Segment
Plane	Midpoint	Bisector	Tri sector  (A only)
Opposite rays	Angle	Collinear	Non collinear
Coplanar	Non coplanar	Right angle	Obtuse angle
Straight angle	Degree	Protractor	Compass
Straight edge	Parallel lines	Perpendicular lines	Skew lines
Locus (A only)	Linear pair	Vertical angles	Complimentary
Supplementary	Adjacent angles	Consecutive (A and B only)	Interior
Corresponding	Alternate interior	Alternate exterior	Same side interior
Same side exterior	Reflexive	Symmetric	Transitive
Substitution	Conditional statement	Converse	Hypothesis
Conclusion	Bi-conditional (A only)	Contra positive (A Only)	Inverse (A only)
Equiangular	Scalene	Isosceles	Equilateral
Median	Angle bisector	Perpendicular bisector	Altitude
SSS	RHL	SAS	ASA
AAS	Interior/Exterior angles	Included side/angle	Opposite side/angle
Inequality theorem	Triangle inequality	Hinge theorem	Rigid motion
Means	Extremes	Ratio	Proportion
Scale factor	Leg	Hypotenuse	Pythagorean triple
Law of sines (A and B only)	Sine	Cosine	Tangent
Angle of elevation (A only)	Angle of depression (A only)	Parallelogram	Rhombus
Rectangle	Trapezoid	Square	Kite
Venn diagram	Diagonal	Apothem	Radius
Center	Chord	Diameter	Circumference
Area	Arc	Sector	Segment
Concentric	Inscribed	Central	Tangent
Secant	Base	Height	Base edge
Lateral face/edge	Oblique (A,B only)	Vertex	Height
Hemisphere	Slant height	Foot (A only)	Coordinate plane
Point	x-coordinate	y-coordinate	Intersection
Pre-image (A,C only)	Image	Symmetry	Reflection
Rotation	Translation	Dilation	Random probability
Sample space (A only)	Independent event (A only)	Mutually exclusive (A only)	Determinant (A only)
Element (A only)	Dimension (A only)	Matrix (A only)	Row (A only)
Column (A only)	Square matrix (A only)	Order (A only)

Units of Study

Geometric Terms

Angles

Measurement

Lines

Intersecting Lines

Transversal

Algebra

Conditional Statements

Triangle Segments

Congruence

Inequalities

Polygons

Triangles

Pythagorean Theorem

Right Triangles

Trigonometric  Ratios

Quadrilaterals

Circles

3-D Figures

Equations of Lines

Transformations

Basic Probability (A only)

Matricies