If a triangle has side lengths a, b, and c, and if a2 + b2 = c2 then the converse of the Pythagorean Theorem says that the triangle is a _______________.
A. scalene triangle
B. equiangular triangle
C. equilateral triangle
D. right triangle
2007-01-06 02:15:39 · 14 answers · asked by Rattiesrule 2 in Science & Mathematics ➔ Mathematics
right triangle
2007-01-06 02:18:09 · answer #1 · answered by noni 2 · 0⤊ 0⤋
A right triangle. The Pythagorean Theorem says that if a right triangle has hypotenuse length c and other side lengths a and b, then c^2 = a^2 + b^2.
For a statement of the form "If A, then B", the converse is "If B, then A". Here the Pythagorean Theorem says "If it is a right triangle, c^2 = a^2 + b^2", so the converse is "If c^2 = a^2 + b^2, it is a right triangle."
2007-01-06 10:19:39 · answer #2 · answered by Scarlet Manuka 7 · 1⤊ 0⤋
D. Right triangle. This is easily proven by constructin a line segment = AB = a and then erecting a perpedicular to AB at A. Extend this perpendicular to C making AC= a. Then connect C to B forming a right triangle. Since since a^2+b^2 = c^2 in both the originatriangle and the newly constructed right triangle then hc c's are also =. Therefore the two triangles are congruent and the original triangle must be a right triangle.
2007-01-06 10:31:09 · answer #3 · answered by ironduke8159 7 · 1⤊ 0⤋
I assume the guy who answered D is right, but technically he's not, because a2 does not mean a squared. It just means twice a. Math is very precise and exact. You have to say EXACTLY what you mean, or your answer will be totally off. In this case, there is too little info. If you also said a does not equal b, then A would be correct. Scalene. In the interest of your homework, answer D.
2007-01-06 10:25:53 · answer #4 · answered by Chick in Florida 1 · 2⤊ 0⤋
D
The Pythagorean theorem is the formula for the right triangle
2007-01-06 13:04:33 · answer #5 · answered by Anonymous · 0⤊ 0⤋
A right triangle.... You know, this looks like your homework. I think you should open up your textbook to the page you covered in class and read the theorem?
2007-01-06 10:42:22 · answer #6 · answered by estratheom 1 · 1⤊ 0⤋
According to my solutions and computations the correct answer is not A nor B neither C but letter D.right triangle......
this is proven and tested by the math department
2007-01-06 10:59:07 · answer #7 · answered by jenny D 1 · 1⤊ 0⤋
By definition, it is a right triangle, because the square of the hypotenuese, c, is equal to the sum of the squares of the other two sides.
2007-01-06 10:25:46 · answer #8 · answered by fangtaiyang 7 · 0⤊ 0⤋
D. right triangle
2007-01-06 10:25:57 · answer #9 · answered by Baddgyaal 2 · 1⤊ 0⤋
Right angled triangle.
2007-01-06 10:24:14 · answer #10 · answered by AAK 2 · 0⤊ 0⤋
a^2+b^2=c^2 only works for right triangles, however, a more complete formula:
a^2=b^2+c^2-2bc*cos(alpha) works for -all- triangles.
2007-01-06 10:30:18 · answer #11 · answered by Kilroy 4 · 0⤊ 0⤋