where students teach themselves
A comprehensive geometry curriculum
Geometry for School and Home
Objectives: Use the Pythagorean Theorem to find the lengths of sides in right triangles. Write exact answers and simplify radicals.
Objectives: Use the Pythagorean Converse to determine if three numbers are the lengths of the sides of a right triangle. Use the Pythagorean Converse to classify triangles as acute, right, and obtuse.
Objectives: Use the Pythagorean Theorem to find lengths of diagonals of faces of rectangular solids. Calculate the length of a diagonal of a rectangular solid.
Objective: Develop and apply theorems relating the lengths of sides in isosceles right triangles.
Objectives: Apply the isosceles right triangle theorems. Use the isosceles right triangle theorems to find lengths of diagonals and sides in squares.
Objective: Develop and apply theorems relating the lengths of sides in 30-60 right triangles.
Objective: Use theorems to find the lengths of the short leg, long leg, and hypotenuse in a 30-60 right triangle given the length of one side.
Objectives: Name the acute angles in right triangles. Identify the hypotenuse and the opposite and adjacent legs for the acute angles in right triangles.
Objectives: Write ratios in right triangles. Complete trigonometric equations for the sin, cos, and tan ratios of acute angles in right triangles.
Objective: Measure sides of right triangles with given acute angle measures and calculate approximations of the sin, cos, and tan ratios for the angle measures.
Objective: Choose the appropriate trigonometric functions to complete equations in order to find lengths of sides in right triangles.
Objective: Find angle measures for values of given ratios using trigonometric inverses. .Complete and solve equations to find angle measures in right triangles using trigonometric inverses.
Objective: Write and solve equations to find all side lengths and angle measures in right triangles.
Objective: Make sketches and write trigonometric and inverse trigonometric equations to solve application problems.
Objective: Develop and apply the Law of Sines for finding side lengths and angle measures in triangles.
Objective: Use the Pythagorean Theorem to find the lengths of sides in right triangles. Approximate answers that are not whole numbers.
Objectives: Name the legs and hypotenuses of right triangles. Measure the legs and hypotenuse of right triangles. Develop a theorem comparing the sum of the squares of the lengths of the legs with the square of the length of the hypotenuse.
Objectives: Use the Pythagorean Theorem to find lengths of diagonals and sides in rectangles, and lengths of altitudes and bases in isosceles triangles.
Objective: Complete factor trees. Simplify square roots using factor trees.
Objective: Complete and solve given trigonometric equations using proportions and cross-products.
Objective: Calculate the sin, cos, and tan ratios for angle measures of 30, 45, and 60 using the isosceles right triangle and 30-60 right triangle theorems. Use a table of trigonometric values to find values of ratios for other given angle measures.