use indirect proof to prove that a triangle cannot have two right angles?

Answer 1

A triangle has 180 degrees. a right angle is 90 degrees. a triangle has 3 angles.

Answer 2

Indirect method:
Let us assume that a triangle has two right angles.
Sum of two right angles=180 degrees
Since the sum of all the angles of a triangle is 180 degrees, the third angle is obviously 0 degrees.
Since there cannot be a triangle with one angle 0 degrees, therefore our assumption is wrong.
Therefore, it is proved that a triangle cannot have two right angles.

Another Method.
If two angles are right angles then they are parallel to each other as they are perpendicular to the same line.
If they are parallel, means they do not intersect.
If they do not intersect there is no third vertice and hence it does not form a triangle.

Answer 3

Suppose a triangle has two right angles.

The sum of those two angles is 180 degrees.

Therefore, the third angle must be 0 degrees (so that the total of the three angles is 180).

But if the third angle is 0 degrees, then the figure is not a triangle. (all angles of a triangle must be greater that 0).

So the initial assumption (that we had a triangle with two right angles) is impossible, because it led us to an inconsistency).

End of indirect proof.

Answer 4

The sum of a triangle's angels is 180degrees. And a triangle has to have 3 ANGLES. The largest one being 90degrees, no other angle can be a 90, else they'd have only 2 angles and not three. Therefore, if a triangle is a right angled (90 degrees) triangle, the other two angles will add up to 90, without one being possible to be 90 itself.

GoodLuck!

Answer 5

right angle =90 degrees
2 right angles=180 degrees
we know that the sum of all the angles of a triangle =180 degrees
if a triangle in which two angles are 90 degrees the third has to bbe zero degrees.
so it wont be a trangle any more it will merge into a straight line.
so there cant be two right angle triangles in a triangle

Answer 6

let the triangle have 2 right angles and let the third angle be x
by the angle sum property of the triangle
90+90+x=180
x=180-90-90
=0
since this is absurd our assumption that there can be two rt. angles in a triangle is wrong

Answer 7

the 1st step in an oblique data is to think of the choice of what you choose to coach. Then follow logical reasoning till you attain a contradiction. State the contradiction. The say subsequently regardless of you're proving is actual. a million. assume line a is parallel to line b. via the replace outdoors attitude theorem attitude a million is congruent to attitude 2. This contradicts the provided that attitude a million is decrease than attitude 2. subsequently line a isn't parallel to line b. 2. assume attitude B =ninety. Base angles of an isosceles triangle are congruent so attitude C = ninety. The sum of the angles of a triangle is a hundred and eighty levels. so attitude A + attitude B + attitude C=a hundred and eighty. via substitution attitude A + ninety + ninety = a hundred and eighty this could be a contradiction because of the fact attitude A won't be able to = 0. subsequently attitude B no longer equivalent ninety and attitude C no longer equivalent ninety. 3. assume that MP is a recommend. via definition of a recommend P is a midpoint. via definition of a midpoint NP = LP this contradicts the provided that NP>LP. subsequently, MP isn't a recommend.

Answer 8

triangle=180 degrees
A+B+C=180
therefore because a triangle has 3 angles if
3X90=270
3X90=not equal to 180

Answer 9

3 angles make 180 degress.
2 right angles is already 180 degrees

Answer 10

tri has 2 sides if any 2 angles are 90 then the third angle has to be zero. then it will no longer be a triangle...........................