Alaska flagAlaska: Similarity, Right Triangles, and Trigonometry Math Standards

2 standards · 11 domains

VERIFY EXPERIMENTALLY THE PROPERTIES OF DILATIONS GIVEN BY A CENTER AND A SCALE FACTOR:

  • G-SRT.1.a 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.
  • G-SRT.1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

(+) PROVE THE LAWS OF SINES AND COSINES AND USE THEM TO SOLVE PROBLEMS.

    (+) 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).

      GIVEN TWO FIGURES, USE THE DEFINITION OF SIMILARITY IN TERMS OF TRANSFORMATIONS TO EXPLAIN WHETHER OR NOT THEY ARE SIMILAR.

        USE THE PROPERTIES OF SIMILARITY TRANSFORMATIONS TO ESTABLISH THE AA CRITERION FOR TWO TRIANGLES TO BE SIMILAR.

          PROVE THEOREMS ABOUT TRIANGLES. THEOREMS INCLUDE: A LINE PARALLEL TO ONE SIDE OF A TRIANGLE DIVIDES THE OTHER TWO PROPORTIONALLY, AND CONVERSELY.

            APPLY CONGRUENCE AND SIMILARITY PROPERTIES AND PROVE RELATIONSHIPS INVOLVING TRIANGLES AND OTHER GEOMETRIC FIGURES.

              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.

                EXPLAIN AND USE THE RELATIONSHIP BETWEEN THE SINE AND COSINE OF COMPLEMENTARY ANGLES.

                  USE TRIGONOMETRIC RATIOS AND THE PYTHAGOREAN THEOREM TO SOLVE RIGHT TRIANGLES IN APPLIED PROBLEMS.

                    (+) 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.

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