High School: Geometry
HSG.SRT.B4
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
October 1, 2018HSG.SRT.B5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
October 1, 2018HSG.SRT.C6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
October 1, 2018HSG.SRT.C7
Explain and use the relationship between the sine and cosine of complementary angles.
October 1, 2018HSG.SRT.C8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
October 1, 2018HSG.SRT.D9
(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
October 1, 2018HSG.SRT.D11
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
October 1, 2018HSG.MG.A1
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*
October 1, 2018HSG.MG.A2
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*
October 1, 2018HSG.MG.A3
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*
October 1, 2018HSG.SRT.A1
Verify experimentally the properties of dilations given by a center and a scale factor:
October 1, 2018