Download Secondary Honors Geometry Objectives

Secondary Honors Geometry Objectives
Chapter 1 – Basics of Geometry
Students will learn about the basic elements of geometry, including how to use
inductive reasoning, how to measure segments and angles, how to bisect a
segment or angle, and the relationships among special pairs of angles.
• Analyze geometric patterns to develop formulas and communicate how the formulas were
derived.
• Model and solve geometric situations using algebraic properties.
• Find the length, midpoint and slope of a segment given the coordinates of the endpoints.
• Use accepted geometric notations.
• Identify angle pairs as adjacent, complementary, supplementary, a linear pair, or vertical
angles.
• Classify angles as acute, right, obtuse or straight.
• Constructing angle and segment bisectors
• Performing constructions to copy segments and angles.
• Finding the area of polygons and circles.
• Finding the perimeter and circumference of polygons and circles.
Chapter 2 – Reasoning and Proof
Students will solve problems by recognizing, analyzing, and writing logical
arguments.
• Write conditional statements, converses, and inverses and determine the truth value of the
statements.
• Prove a statement false by using a counterexample.
• Recognize and develop different styles of proof using deductive reasoning.
• Apply reasoning skills to develop an algebraic proof.
• Use symbolic notation to form conclusions by applying the laws of logic to true statements.
Chapter 3 – Perpendicular and Parallel Lines
Students will investigate the relationships between lines and angles on a plane
and in space.
• Write an equation of a line perpendicular or parallel to a line through a given point.
• Model and solve geometric situations using algebraic properties.
• Prove lines parallel or perpendicular using slope or angle relationships.
• Recognize and develop different styles of proof using deductive reasoning.
• Differentiate between parallel, perpendicular, skew, and intersecting lines.
• Classify angle pairs formed by two lines and a transversal.
• Constructing parallel and perpendicular lines.
Chapter 4– Congruent Triangles
Students will classify and prove triangles congruent given information about their
sides and angles.
• Model and solve geometric situation using algebraic properties.
• Prove congruency and similarity of geometric figures
• Recognize and develop different styles of proof using deductive reasoning.
• Classify and use the properties of acute, right, scalene, oblique, isosceles,
equilateral, or equiangular triangles.
• Constructing congruent figures using basic construction techniques.
Chapter 5– Properties of Triangles
Students will investigate the properties of bisectors, medians, altitudes, and midsegments of a triangle and how those properties relate to triangles. Students will
also investigate various triangle inequalities.
• Model and solve geometric situations using algebraic properties.
• Identify medians, altitudes, and angle bisectors of a triangle and the perpendicular
bisectors of the sides of a triangle.
• Identify and apply the properties of mid-segments of triangles and trapezoids.
• Identify and apply the properties of perpendicular bisectors and angle bisectors.
• Constructing perpendicular lines through a point.
• Constructing points of concurrency.
Chapter 6– Quadrilaterals
Students will study quadrilaterals, their properties and will apply those properties
to solve geometric problems.
• Model and solve geometric situations using algebraic properties.
• Develop reasoning skills to prove a quadrilateral as a parallelogram, trapezoid,
rectangle, square, rhombus, kite or none of the above.
• Recognize and develop different styles of proof using deductive reasoning.
• Identify the properties of polygons and quadrilaterals.
• Identify and apply the properties of mid-segments of triangles and trapezoids.
• Verify the classifications of geometric figures using coordinate geometry to find
lengths and slopes.
Chapter 7 – Transformations
Students will learn about transformations, including the three ways to describe
motion of geometric figures in the plane and how to use transformations in reallife situations.
• Identify and define vectors related to transformations.
• Perform & analyze transformations (translations, rotations, reflections, and
dilations) using coordinate geometry
• Analyzing problems using vectors and vector operations.
• Translate, reflect, and rotate geometric figures.
Chapter 8 – Similarity
Students will learn about similar polygons, including four ways to prove triangles
are similar given information about their sides and angles and how to use similar
polygons to solve real-life problems.
• Set up ratios and solve proportions for given similar geometric shapes.
• Prove congruency and similarity of geometric figures.
• Apply ratios and proportions to solve problems using the properties of similar
figures.
• Apply Geometric Mean in problems involving proportions.
• Dilating geometric figures.
Chapter 9 – Right Triangles and Trigonometry
Students will learn about right triangles and trigonometry, including properties
related to general right triangles, similar right triangles, and special right
triangles. They will also learn applications of right triangles (trigonometry),
triangle measurement, and vectors.
• Identify trigonometric relationships (sine, cosine, & tangent) using right triangles,
expressing the relationships as fractions or decimals.
• Solve problems using the properties of special right triangles.
• Find the angle measure in degrees given the trigonometric ratio using a calculator.
• Find the trigonometric ratio given the angle measure in degrees using a calculator.
• Find the missing measures of right triangles.
• Solve real-world problems using trigonometric ratios and properties of congruent
and similar figures.
• Apply Geometric Mean in problems involving proportions.
• Deriving the Pythagorean Theorem from the distance formula.
• Analyzing the problems using vectors and vector operations.
Chapter 10 – Circles
Students will learn about the properties of segments, angles, and arcs related to
circles.
• Graph a circle given the equation in the form (x – h)2 + (y – k)2 = r2
• Write the equation of a circle given its graph.
• Identify the relationships between the measures of intercepted arcs and angles in a
circle.
• Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed
angles, and tangents for circles.
• Apply appropriate theorems to find segment lengths in circles.
• Deriving the equation of a circle from the distance formula.
• Finding the Loci based on given measurements.
Chapter 11 – Area of Polygons and Circles
Students will learn about areas of polygons and circles, including how to find
angle measures and areas of polygons, how to compare perimeters and areas of
similar figures, and how to find the circumference and area of a circle.
• Identifying the effect on area or volume when working with similar figures.
• Define pi as the ratio of the circumference to the diameter of a circle.
• Find the circumference and arc length.
• Find the area of the sector of a circle.
• Find the area of an irregular region.
• Calculate and find the measures of the interior and exterior angles of regular
polygons.
• Identifying the effect on area or volume when working with similar figures.
Chapter 12 – Surface Area and Volume
Students will learn about surface area and volume of solids, including how to
calculate and use surface area and volume of various solids in real-life situations.
• Classify regular polyhedrons.
• Find the surface area and volume for prisms, cylinders, pyramids, cones, and
spheres given the formula.
• Identifying the effect on area or volume when working with similar figures.