Theorem: A triangle has at most one obtuse angle.
Eduardo is proving the theorem above by
contradiction. He began by assuming that in
triangleABC, angleA and angleB are both obtuse. Which
theorem will Eduardo use to reach a
contradiction?
A If two angles of a triangle are equal, the sides
opposite the angles are equal.
B If two supplementary angles are equal, the
angles each measure 90°.
C The largest angle in a triangle is opposite the
longest side.
D The sum of the measures of the angles of a
triangle is 180°.
is it A, B, C, or D? i am confused.. haha thanks! =]
2007-04-06 17:55:55 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
the answer is D, because no matter obtuse, scalene, equilateral or right triangle the sum of the 3 angles always equal to 180°
2007-04-06 19:50:15 · answer #1 · answered by Anonymous · 0⤊ 1⤋
The sum of the angles of a triangle is 180 degrees.
Since an obtuse angle > 90 degrees, then two obtuse angles would be greater than 180 degrees, thus violating the above proven theorem
2007-04-06 18:04:30 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
He will certainly use D.
To expand on this, Eduardo will use D to instantly see the contradiction.
An obtuse angle is an angle of > 90 degrees. If angle A and angle B are both obtuse, then A + B > 180.
But, you know that the angles of a triangle measure 180. Thus, you cannot have two angles that add up to over 180 in a triangle.
2007-04-06 18:00:52 · answer #3 · answered by Rev Kev 5 · 0⤊ 0⤋
He is trying to contradict 'both angles are obtuse'
You need to know that an obtuse angle has a measure greater than 90 degrees.
There is no mention of these angles being congruent (isosceles) or supplementary. In fact, only one answer could contradict having two angles with measures greater than 90.
I think I'll let you figure which one....
2007-04-06 18:41:51 · answer #4 · answered by suesysgoddess 6 · 1⤊ 0⤋
D
because if you have two obtuse angles
i.e. angle>90
then we have a problem which is
the total sum of angles in a triangle is 180 but if we have two angles greater than 90 then the sum of two angles itself exceeds 180 and you can forget about adding the third angle..:)
2007-04-06 18:04:26 · answer #5 · answered by crazytaco 2 · 1⤊ 0⤋
D.
Obtuse means more than 90 degrees.
So if we had more than one over 90 degrees, the sum of all three must equal 180 degrees, and with just two angles, it is already too much.
2007-04-06 18:01:59 · answer #6 · answered by Anonymous · 0⤊ 0⤋
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2016-12-08 20:30:50 · answer #7 · answered by ? 4 · 0⤊ 0⤋
The ans is
D
as if there will be more than one OBTUSE ANGLE
the sum will cross 180 which is not possible and hence contradiction achieved
2007-04-06 18:10:38 · answer #8 · answered by nitro_khan 2 · 1⤊ 0⤋