Triangles: Properties, Theorems, and Formulas
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Questions and Answers

What is the sum of the interior angles of a triangle?

  • 360 degrees
  • 180 degrees (correct)
  • 120 degrees
  • 240 degrees
  • What is the formula to calculate the area of a triangle using the lengths of its sides?

  • a × b
  • √(a^2 + b^2 + c^2)
  • a + b + c
  • √(s(s-a)(s-b)(s-c)) where s is the semi-perimeter (correct)
  • What is the name of the line segment that divides an angle into two equal parts?

  • Perimeter
  • Angle Bisector (correct)
  • Altitude
  • Median
  • What is the name of the triangle with one right angle (90 degrees)?

    <p>Right Triangle</p> Signup and view all the answers

    What is the name of the theorem that states the sum of the lengths of any two sides is greater than the length of the third side?

    <p>Triangle Inequality Theorem</p> Signup and view all the answers

    Study Notes

    Definition

    • A triangle is a polygon with three sides and three vertices.
    • It is a closed shape with three straight sides.

    Types of Triangles

    • Equilateral Triangle: A triangle with all sides of equal length.
    • Isosceles Triangle: A triangle with two sides of equal length.
    • Scalene Triangle: A triangle with all sides of different lengths.
    • Right Triangle: A triangle with one right angle (90 degrees).
    • Oblique Triangle: A triangle that is not a right triangle.
    • Acute Triangle: A triangle with all angles acute (less than 90 degrees).
    • Obtuse Triangle: A triangle with one obtuse angle (greater than 90 degrees).

    Properties

    • Perimeter: The sum of the lengths of all three sides.
    • Area: The region inside the triangle, calculated using various formulas (e.g. base × height, Heron's formula).
    • Angles: The sum of the interior angles is always 180 degrees.
    • Altitude: The distance from a vertex to the opposite side.
    • Median: The line segment from a vertex to the midpoint of the opposite side.
    • Angle Bisector: The line segment that divides an angle into two equal parts.

    Theorems and Formulas

    • Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse of a right triangle.
    • Triangle Inequality Theorem: The sum of the lengths of any two sides is greater than the length of the third side.
    • Heron's Formula: The area of a triangle can be calculated using the lengths of its sides.
    • Law of Cosines: A formula relating the lengths of the sides and the cosine of one of the angles.

    Special Triangles

    • 30-60-90 Triangle: A right triangle with angles of 30, 60, and 90 degrees.
    • 45-45-90 Triangle: A right triangle with angles of 45, 45, and 90 degrees.
    • 3-4-5 Triangle: A right triangle with sides of length 3, 4, and 5 units.

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    Description

    Test your knowledge of triangles, including types, properties, theorems, and formulas. Learn about equilateral, isosceles, scalene, right, and oblique triangles, as well as perimeter, area, angles, and special triangles.

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