High School: Geometry
HSG.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, 2018HSG.SRT.A1a
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
October 1, 2018HSG.SRT.A1b
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
October 1, 2018HSG.SRT.A2
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
October 1, 2018HSG.SRT.A3
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
October 1, 2018HSG.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, 2018