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Topic: Triangles 

Mathematics

 Standard 4.  Understands and applies basic and advanced properties of the concepts of measurement
  Level IV (Grade 9-12)
   Benchmark 3.Selects and uses an appropriate direct or indirect method of measurement in a given situation (e.g., uses properties of similar triangles to measure indirectly the height of an inaccessible object)
    Knowledge/skill statements
     1.Uses the properties of triangles to measure the height of distant object
     2.Understands the concept of indirect measurement using computations
     3.Understands the concept of direct measurement
 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level III (Grade 6-8)
   Benchmark 3.Understands the defining properties of triangles (e.g., the sum of the measures of two sides of a triangle must be greater than the measure of the third side)
    Knowledge/skill statements
     1.Understands that the sum of two sides of a triangle must be greater than the measure of the third side
     2.Understands the properties of triangles
   Benchmark 7.Understands the basic concept of the Pythagorean theorem
    Knowledge/skill statements
     1.Understands the concept of the Pythagorean theorem
  Level IV (Grade 9-12)
   Benchmark 2.Use the Pythagorean theorem and its converse and properties of special right triangles (e.g. 30° - 60° - 90° triangle) to solve mathematical and real-world problems
    Knowledge/skill statements
     1.Determines whether a problem can be solved by the Pythagorean theorem
     2.Understands the properties of 30° - 60° - 90° triangles
     3.Understand the properties of 45° - 45° - 90° triangles
     4.Determines whether a problem can be solved by making use of the properties of 30° - 60° - 90° triangles
     5.Determines whether a problem can be solved by making use of the properties of 45° - 45° - 90° triangles
   Benchmark 7.Understands the basic concepts of right triangle trigonometry (e.g., basic trigonometric ratios such as sine, cosine, and tangent)
    Knowledge/skill statements
     1.Understands the concept of right triangle trigonometry