**Benchmark
9C: The Mathematical World - Shapes**
**(grades 9-12, page 225)**
Distances and angles that are inconvenient to measure directly can be found
from measurable distances and angles using scale drawings or formulas.
(1 of 4)
Standard 7-2 page 157, Grades 9-12

Represent problem situations with geometric models and apply properties
of figures
Standard 9-1 page 163, Grades 9-12

Apply trigonometry to problem situations involving triangles

There are formulas for calculating the surface areas and volumes of regular
shapes. When the linear size of a shape changes by some factor, its area
and volume change disproportionately: area in proportion to the square
of the factor, and volume in proportion to its cube. Properties of an object
that depend on its area or volume also change disproportionately. (2 of
4)
Standard 7-4 page 157, Grades 9-12

Deduce properties of, and relationships between, figures from given
assumptions
Geometric shapes and relationships can be described in terms of symbols
and numbers -and vice versa. For example, the position of any point on
a surface can be specified by two numbers; a graph represents all the values
that satisfy an equation; and if two equations have to be satisfied at
the same time, the values that satisfy them both will be found where their
graphs intersect. (3 of 4)
Standard 8-1 page 161, Grades 9-12

Translate between synthetic and coordinate representations
Standard 8-3 page 161, Grades 9-12

Identify congruent and similar figures using transformations

Different ways to map a curved surface (like the earth's) onto a flat surface
have different advantages. (4 of 4)
Standard 7-2 page 157, Grades 9-12

Represent problem situations with geometric models and apply properties
of figures