Question

hota mates....

state and prove the angle sum property of a triangle....
plz explain nicely.... & plz don't do on paper...!!!

thanks for the help... ☺

Answer 1

Hey Dear Here Is Your Ansr... !!

~~~Angle sum property of triangle states that, sum of interior angles of a triangle is 180°. 

prove 
Start with the following triangle with arbitrary values for the angles:

~~~~Angle sum theorem
Since angle a, angle b, and angle c make a straight line,

angle a + angle b + angle c = 180 degrees

~~~~Since alternate interior angles are equal, angle a = angle x and angle b = angle y

~~~Therefore, angle x + angle y + angle c = 180 degrees ...

Hope u get it...

Answer 2

To Prove :- Sum of all angles of triangle is equal to 180° .


Proof - Let ABC be a ∆ , as shown in the figure .

Construct - Draw a line MN parallel to side BC of the given triangle .


Since MN is a straight line , it can be concluded that :

∠MAB + ∠BAC + ∠NAC = 180°  ……… (1)

SinceMN||BC and AB, AC are transversals,

Therefore, ∠NAC = ∠ACB (a pair of alternate angle)

Also, ∠MAB = ∠CBA (a pair of alternate angle)

Substituting the value of ∠NAC and∠MAB in equation (1),

∠ACB + ∠BAC + ∠CBA= 180°

Thus, the sum of the interior angles of a triangle is 180°.