angles of a triangle sum up to 180 degrees. can you prove it?

Answer 1

This is a good question
Consider a straight line ABC Labc - 180 degrees,
here anlge LBAC = 0 and LBCA = 0 and LABC = 180 deg
Consider another similar triangle ABC' where LBAC tends to 0. In this case LABC tends to 180 so the sum of the angles
of a triangle tends to 180 degrees under limits of continuity.

Thx,
Gopal S




Thx,
Gopal S

Answer 2

Consider any triangle ABC.

Suppose that you walk along AB.

At B, you turn through an angle α toward C. The interior angle is now 180- α,

On reaching B, you turn through an angle β. As before the interior angle is 180- β.

On reaching A, you turn through an angle γ. As before the interior angle is 180- γ.

Since you are at the initial point and in the initial direction, the total angle you turned is 360°.

That is α + β + γ = 360°..

The sum of the interior angle that is the sum of the angles of the triangle is

180- α + 180- β + 180- γ
= 540 - [α + β + γ ]
= 540 - 360
= 180°.
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Or

In the triangle ABC, the direction AB is turned through α toward C.

The angle ABC = 180- α,

Similarly the angle BCA = 180- β and angle CAB = 180- β

Since the final direction is initial direction.

α + β + γ = 360°..

The sum of the interior angle that is the sum of the angles of the triangle is

180- α + 180- β + 180- γ
= 540 - [α + β + γ ]
= 540 - 360
= 180°.
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This can be extended to any N sided figure.

In an N sided figure, we take n turns.

The sum of the angles turned = [a + b + c + ...+ n] = 360 °.

The sum of the interior angles = N 180 - [a + b + c + ...+ n]

= 180 [N - 2].

For triangle N = 3 and hence

the sum of the angles = 180*1 .

For square 180 *2 etc.

Answer 3

30 - 60 - 90 Triangle

45 - 45 - 90 Triangle

The sum of the triangle equals 180 degrees

- - - - - - - -s-

Answer 4

Let the triangle be ABC.I imagine the line AB to be horizontal for convenience. Extend AB past B to any point D. Also, let BE be a line parallel to AC and on the same side of AB as C. Then angle ACB is equal to angle CBE by alternate interior angles. Angle EBD is equal to angle BAC by corresponding angles. But now, the sum of the angles of ABC is equal to the straight angle ABD.

Answer 5

Take a Triangle ABC

Now draw a line XY parallel to line BC and passing through the point A of ∆ABC

Now,
∠ACB = ∠CAY [ int. alternet angles ] → (i)
∠ABC = ∠BAX [ int. alternet angles ] →(ii)

Now,
∠ACB + ∠BAC +∠ABC = 180⁰ [angles on a strait line is 180⁰]

∴ now replace ∠ACB with ∠CAY & ∠ABC with ∠BAX
∵ we have proved the given pairs equal (from i & ii)

NOW WE GET ,
∠ABC + ∠BCA + ∠CAB = 180⁰

proved......

Answer 6

I upload somthing for u
http://i17.tinypic.com/4vg4d38.jpg
It's a shape. look at this and then read my explanation.
In this pic you can see a=d , b=c , and a+b+k=180

Answer 7

I, persay, can't prove it, but we all know it's true. Yes, I've had plane geometry and drafting as well. Those problems, to solve, were in 'trig' though, I think