Foundations of Geometry

• Define deductive and inductive reasoning as well as proofs and axiomatic systems.
• Identify points, lines, and planes.
• Describe segments, rays, and angles.
• Formulate geometric proofs.
• Construct perpendicular lines and angle bisector.

Triangles

• Classify triangles by their sides and angles.
• Use geometric theorems to prove how triangles are congruent.
• Construct a triangle congruent to a given triangle.
• Use congruent and right triangles to prove statements and theorems.
• Construct triangles including altitude and the median parts.

Parallel Lines and Polygons

• Define parallel lines, transversals, and angles.
• Identify different types of polygons and their components.

Quadrilaterals

• Describe the characteristics of a quadrilateral.
• Apply the properties of parallelograms.
• Use the properties of special quadrilaterals.
• Examine the properties of trapezoids.

Similar Polygons and the Pythagorean Theorem

• Define ratio, proportion, and proportional segments.
• Apply the postulates and theorems of similar polygons.
• Construct proportional segments of polygons.
• Demonstrate the applications of the Pythagorean Theorem.

Circles

• Define a circle and related terms.
• Describe the theorems of chords and secants of circles.
• Construct a tangent to a circle and measure angles formed by tangents.

Areas of Polygons and Circles

• Determine areas of quadrilaterals.
• Calculate the circumference and area of circles.
• Identify area and arc length of a sector.
• Apply the area formula to regular polygons.

Solid Geometry

• Identify the behavior of lines and planes in space.
• Define solid figures that form in space.
• Calculate the surface area and volume of prisms, pyramids, cylinders, cones, and spheres.

Introduction to Analytic Geometry

• Identify the relationship between geometry and algebra.
• Define the Cartesian coordinate system.
• Calculate the length and midpoint of a line segment.
• Identify the slope of the line, point-slope form, and slope-intercept form of a line.

Introduction to Trigonometry

• Define the sine, cosine, and tangent of an acute angle.
• Identify the use of sine, cosine, and tangent in special right triangles.
• Calculate the missing sides in a right triangle.
• Define solving triangles.
• Determine the area and perimeter of figures using trigonometry.
• Apply sine, cosine, and tangent to real-life problems.

Review Topics and Objectives from All Workshops