where students teach themselves
A comprehensive geometry curriculum
Geometry for School and Home
Objectives: Develop and apply a theorem about lengths of chords and their distance from the center of a circle. Use the Pythagorean Theorem to calculate lengths of chords, radii, and distances from centers of circles.
Objectives: Identify tangents, points of tangency, and secants. Apply the theorem that a tangent is perpendicular to a radius drawn to the point of tangency.
Objectives: Name central angles. Name arcs intercepted by central angles. Name minor and major arcs determined by two points on a circle. Name semicircles.
Objectives: Find measures of arcs by measuring central angles with a protractor. Write measures of minor arcs and calculate measures of major arcs using measures of central angles.
Objectives: Calculate measures of arcs using addition or subtraction of given arc measures. Calculate measures of arcs in circles with diameters. Calculate measures of arcs in circles with congruent chords.
Objectives: Name arcs intercepted by angles determined by secants, tangents, and chords in circles. Name inscribed angles and their intercepted arcs.
Objectives: Develop and apply a theorem relating the measure of an inscribed angle to the measure of its intercepted arc. Apply a theorem relating the measure of an angle with its vertex at the intersection of a chord and a tangent to the measure of its intercepted arc.
Objective: Develop and apply a theorem relating the measures of vertical angles in a circle and the measures of their intercepted arcs.
Objective: Develop and apply theorems relating angles in the exterior of circles and their intercepted arcs.
Objectives: Calculate the circumference of a circle given the radius or diameter. Calculate the radius and diameter of a circle given the circumference.
Objectives: Use measurement to determine the relationship between circumferences and diameters of circles. Calculate an approximate value of pi
Objectives: Calculate lengths of arcs given arc measures and radius or diameter. Calculate arc measures given arc lengths and radius or diameter.
Objectives: Develop and apply the formula for the area of a circle. Calculate the circumference of a circle given its area. Calculate the area of a circle given its circumference.
Objective: Develop and apply methods and formulas for finding the area of sectors of circles.
Objectives: Apply a formula for areas of rings. Find areas of figures that are composites of circles and polygons. Find areas of segments of circles with right central angles.
Objective: Apply formulas for surface area of right cylinders, cones, and spheres.
Objective: Develop and apply postulates and theorems about radii, chords, diameters, and angles in circles.
Objective: Apply formulas for volumes of cylinders, cones, and spheres.
Objectives: Name and identify circles and their centers. Name radii, chords, and diameters in circles. Measure the radius and diameter of circles.
Objective: Develop and apply a theorem relating the lengths of segments of intersecting chords.
Objective: Develop and apply a theorem relating the lengths of segments of intersecting secants.
Objective: Develop and apply a theorem relating the lengths of segments of intersecting tangents and secants.
Objectives: Name tangent segments. Develop and apply a theorem about the lengths of tangent segments with a common endpoint.
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Objectives: Identify and classify tangent circles. Name and classify lines that are tangent to two circles, Calculate distance between centers of tangent circles.
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