Geometry

“Geo-” means “earth” and “-metry” means measure. Much of geometry is about measuring, and also about shapes, their properties and relationships between them. There are many opportunities to explore and investigate geometric concepts and relationships using concrete manipulatives. A

hands-on visual approach is taken. The role of proofs in understanding geometry is clarified.

Comparisons between inductive and deductive reasoning are made. Skills taught are closely related with other branches of mathematics such and algebra and trigonometry. Algebra I is a prerequisite for this course. To be successful in geometry, knowledge of solving equations, sketching graphs, factoring equations, and simplifying radicals is integral.

RESOURCES: McDougal Littell (Larson) Geometry Text

I. Honors Geometry – First Nine Weeks

A. Essentials of Geometry

- Use the undefined terms of points, lines, and planes.
- Use the terms of collinear, coplanar, opposite rays, and intersection.
- Use the definitions of and the symbols for lines,
- segments, rays and distances.
- Know the difference between definitions, postulates and theorems.
- Find the distance between 2 points on a number line.
- Apply the Ruler Postulate and the Segment Addition Postulate.
- Use the distance and midpoint formulas.
- Be able to name, measure, and classify angles.
- Define congruent angles and angle bisectors.
- Apply the Protractor Postulate and the Angle Addition Postulate.
- Define complementary, supplementary and adjacent angles and find their measures.
- Define and identify linear pairs and vertical angles.
- Define polygon, and know the difference between concave, convex, equilateral, and equiangular polygons.
- Identify the vertices and sides of polygons.
- Classify polygons by the number of sides. Know the names of polygons with 3-12 sides.
- Find the perimeter/circumference and area of squares, rectangles, triangles and circles.

B. Reasoning and Proof

- Describe patterns and use inductive reasoning. Make conjectures about those patterns.
- Write definitions as conditional statements. Identify the hypothesis and the conclusion.
- Write the converse, inverse, and contrapositive of conditional statements.
- Define perpendicular lines.
- Be able to write definitions as biconditional statements.
- Be able to determine the difference between the Laws of Logic (Law of Detachment and Law of Syllogism.)
- Use the postulates involving points, lines, and planes.
- Review the properties of Addition, Subtraction, Multiplication, Division, and Substitution. Learn the Reflexive, Symmetric, and Transitive Properties.
- Be able to understand a basic two-column proof. Be able to fill in the missing statements or reasons.
- Use the properties of special pairs of angles, i.e. Congruent Supplements Theorem.

II. Honors Geometry - 2^{nd} Nine Weeks

A. Parallel and Perpendicular Lines

- Define and identify parallel lines, skew lines, and parallel planes.
- Be able to identify angles formed by a transversal, i.e. corresponding, alternate interior, alternate exterior, and same-side interior angles.
- Use angles formed by parallel lines and transversals.
- Use angle relationships to prove that lines are parallel.
- Find and compare slopes of lines. Identify parallel and perpendicular lines.
- Write equations of lines in slope-intercept form and in standard form, given specific scenarios.
- Find the distance between a point and a line.

B. Apply Triangle Sum Properties

- Define Triangle. Classify triangles by their sides and their angles.
- Define interior angles and exterior angles and find the measures of each.
- Learn theorems about angles of triangles.
- Identify corresponding parts of congruent polygons.
- Prove triangles congruent by SSS, SAS, AAS, ASA, and HL.
- Prove triangle congruent doing two-column proofs.
- Use theorems about isosceles and equilateral triangles.

C. Relationships Within Triangles

- Define midsegment of a triangle
- Use properties of midsegments of triangles
- Identify perpendicular bisectors, medians, and altitudes of triangles.
- Use triangle inequalities to find possible side lengths.

D. Similarity

- Solve problems by writing and solving proportions.
- Use proportions to solve geometry problems.
- Use proportions to identify similar polygons.
- Prove triangles congruent by AA, SSS, and SAS Similarity Postulates.
- Use proportions with a triangle or parallel lines.

III. Honors Geometry – 3^{rd} 9 weeks

- Right Triangles and Trigonometry
- Use Pythagorean Theorem to find side lengths in right triangles.
- Learn Pythagorean triples.
- Use the Converse of Pythagorean Theorem to determine if a triangle is a right triangle.
- Use the properties of the altitude of a right triangle.
- Solve missing lengths of sides of 45-45 right triangles and 30-60 right triangles.
- Use trig ratios or inverse trig ratios to find the missing sides or angles of right triangles.
- Use angles of depression and angles of elevations to solve word problems with trig ratios.

- Quadrilaterals

- Find the interior and exterior angle measures of polygons.
- Identify the properties of parallelograms.
- Find the angle and side measures of parallelograms.
- Use the properties to identify parallelograms.
- List and identify properties of rhombuses, rectangles, and squares.
- List and identify properties of trapezoids and kites.
- Be able to classify quadrilaterals based on the properties.

- Properties of Circles

- Define circle, center, radius, diameter, chord, secant and diameter and find their measures.
- Use properties of a tangent to a circle.
- Define central angle, minor arc, major arc, and semicircle and find their measures.
- Use the relationships of arcs and chords in a circle.
- Define inscribed angle and intercepted arc and find their measures.
- Find the measures of angles inside or outside of the circle.
- Find the segment lengths of a circle.
- Write equations of a circle in the coordinate plane.

IV. Honors Geometry – 4^{th} 9 Weeks

A. Compositions of Transformations

- Determine Symmetry of Shapes
- Define image, preimage and isometry.
- Perform reflections over the x- and y-axis and about a given line.
- Rotate a figure 90, 180, and 270 degrees clockwise.
- Translate a figure in all directions.
- Dilate a figure by whole numbers and fractions.
- Do compositions of transformations.

B. Measuring Length and Area

- Find the areas of triangles and parallelograms.
- Find the areas of trapezoids, rhombuses, and kites.
- Use ratios to find areas of similar figures.
- Find the circumference and arc lengths of circles.
- Find the areas of circles and sectors.
- Find the areas of regular polygons inscribed in circles.
- Use lengths and areas to find geometric probabilities.

C. Surface Area and Volume of Solids

- Define polyhedron, faces, edges, and vertices.
- Know Euler’s Theorem.
- Find the surface areas of prisms and cylinders.
- Use nets to predict a shape.
- Find surface areas of pyramids and cones.
- Find the volume of prisms, cylinders, pyramids, and cones.
- Define sphere, center, radius, chord, and diameter.
- Find the surface areas and volumes of spheres