TERMS FOR SPECIAL TRIANGLE PROBLEMS

Scalene Triangle: triangle with no equal sides and no equal angles
Isosceles Triangle: triangle with two equal sides and two equal angles
Equilateral Triangle: triangle with three equal sides and three equal angles
Right Triangle: triangle that contains a 90° angle
45-45-90 Triangle: special triangle with two 45° angles and one 90° angle
30-60-90 Triangle: special triangle with one 30° angle, one 60° angle and one 90° angle

RULES FOR SPECIAL TRIANGLE PROBLEMS

1) Right Triangle Rules:
      a) the longest side, or hypotenuse, is opposite the right angle
      b) (leg1)² + (leg2)² = (hypotenuse)²

            x is the hypotenuse; x² = 8² + 6² --> x² = 64 + 36 --> x² = 100 --> x = 10

2) 45-45-90 Triangle Rules:
      a) two smaller sides are equal
      b) hypotenuse = (smaller side length)(√2)

                 If s = 2, then the sides are 2, 2, and 2√2

3) 30-60-90 Triangle Rules:
      a) the shortest side is opposite the 30° angle
      b) b) the medium side is opposite the 60° angle
      c) c) the longest side is opposite the 90° angle

              If x = 4, then the sides are 4, 8, and 4√3

SAMPLE PRACTICE QUESTION FOR SPECIAL TRIANGLES

1.

If BD bisects AC and AC =10, what is the length of AB?

      Solution
      1) If BD bisects AC, then BD AC and BD bisects angle ABC

      2) Angle BAD = 180° - 90° - 45° = 45°.

      4) Triangle ABD is a 45-45-90 triangle, so hypotenuse AB = 5√2

SAT Math: Special Triangle Problems

Lesson Includes:

—Math Terms for Special Triangles

—Rules for Special Triangles

—Sample Practice Questions

—Practice Questions

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SPECIAL TRIANGLE MATH QUIZ

 

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