Mi Math Standards

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H

HSG-GPE.B.4

Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

09, 10, 11, 12

HSG-GPE.B.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

09, 10, 11, 12

HSG-GPE.B.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

09, 10, 11, 12

HSG-GPE.B.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

09, 10, 11, 12

HSG-MG.A.1

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

09, 10, 11, 12

HSG-MG.A.2

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

09, 10, 11, 12

HSG-MG.A.3

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).*

09, 10, 11, 12

HSG-SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor:

09, 10, 11, 12

HSG-SRT.A.1a

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.

09, 10, 11, 12

HSG-SRT.A.1b

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.