Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Help with this geometry/probability question?

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  • 1 month ago
    Best Answer

    In order for △ABC and △XYZ to be similar, the corresponding angles must be congruent:

    ∠A ≅ ∠X

    ∠B ≅ ∠Y

    ∠C ≅ ∠Z

    PART A:

    Here we assume a scalene triangle. The angles for △XYZ can be arranged in 3! = 6 ways.

    So the probability that everything matches for a scalene triangle (and hence they are similar) is:

    1/6

    PART B:

    Here we have two congruent angles in an isosceles triangle. There would be 3! = 6 ways to arrange the angles, but 2 of them would be identical, so divide by 2. That means there are 3 ways to align the angles with only 1 being right.

    So the probability that everything matches for an isosceles triangle (and hence they are similar) is:

    1/3

    PART C:

    In an equilateral triangle, all the angles are the same (60°), so any arrangement will automatically match.

    The probability that everything matches for an equilateral triangle is:

    1/1

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