The shaded triangle is set inside a pentagon. Is the shaded triangle a right triangle? Complete the statement that answers the question.
Since 9² + 12² =
15², the shaded triangle
is
is not
a right triangle.
The shaded triangle is set inside a pentagon. Is the shaded triangle a right triangle?
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To determine if the shaded triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In your case, you have the lengths 9, 12, and 15.
Calculating:
– 9² = 81
– 12² = 144
– 15² = 225
Now, add 9² and 12²:
81 + 144 = 225
Since 225 equals 15², we find that:
Since 9² + 12² = 15², the shaded triangle is a right triangle.
This means that the triangle has one angle that measures 90 degrees. Well done on this question! If there’s anything else you’d like to ask, just let me know!