Geometry

Students will create and use two- and three-dimensional representations of authentic situations.

Students will solve geometric problems involving inaccessible distances using basic trigonometric principles, including the Law of Sines and the Law of Cosines

Students will prove geometry theorems.

Students will understand and recognize the use of definitions, postulates, and axioms in defining a deductive system such as Euclidean geometry.

Prove the first five propositions in Book I of Euclid's Elements. Construct a regular pentagon with a straight-edge and compass.

Students will compute lengths, areas, and volumes according to historical formulas.

Find the volume of a truncated pyramid using the Babylonian, Chinese, and Egyptian formulas

Compute the areas of regular polygons by Herons formulas.

Identify cyclic quadrilaterals and find associated lengths by Ptolemy's Theorem.

Students will explore and prove statements in non-Euclidean geometry

Prove that the summit angles of an isosceles birectangle are congruent, but that it is impossible to prove they are right without referring to the parallel postulate or one of its consequences

Describe the hypothesis of the acute angle (Hyperbolic), the hypothesis of the right angle (Euclidean), and the hypothesis of the obtuse angle (Spherical).

Prove that under the hypothesis of the acute angle, similarity implies congruence

Students will apply the concepts of area, volume, scale factors, and scale drawings to planning for housing.

Students will apply the distance formula.

Students will apply the properties of angles and segments in circles.