To determine whether a triangle with side lengths 15, 10, and 12 is a right triangle, we need to use the converse of the Pythagorean theorem.
The converse of the Pythagorean theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
In this case, let's designate side lengths 15, 10, and 12 as a, b, and c, respectively, with c being the longest side (as the Pythagorean theorem applies to the hypotenuse of a right triangle).
According to the converse of the Pythagorean theorem, if c^2 = a^2 + b^2, then the triangle with side lengths 15, 10, and 12 is a right triangle.
Let's calculate:
c^2 = 12^2 = 144
a^2 + b^2 = 15^2 + 10^2 = 225 + 100 = 325
Since c^2 is not equal to a^2 + b^2 (144 ≠ 325), the triangle with side lengths 15, 10, and 12 is not a right triangle.
Hence, using the converse of the Pythagorean theorem, we can determine that the triangle with side lengths 15, 10, and 12 is not a right triangle.
using the converse of the Pythagorean theorem explain whether a triangle with the sides of 15,10, and 12 is a right triangle
3 answers
what is a converse of a theorem that is an if-then statement.
the Converse the same as the original theorem
the two parts are negated by using the word not
the If part and the then part switch places
the converse of a theorem has no relationship to the original theorem
the Converse the same as the original theorem
the two parts are negated by using the word not
the If part and the then part switch places
the converse of a theorem has no relationship to the original theorem
The converse of a theorem is when the if and then parts switch places.