Question

in the given figure if angle abc is equal to angle ACB and angle 3 is equal to angle 4 show that angle 1 is equal triangle 2 and also say the euclid's axiom used in it

Answer 1

Answer:

The axiom used is: If equals be subtracted from equals, the remainders are equal

Proof:

The figure is attached

Given ∠ABC = ∠ACB       .......... (1)

And ∠3 = ∠4

or, ∠4 = ∠3          .........................(2)

From the figure, we can see that

∠1 = ∠ABC  - ∠4

and ∠2 = ∠ACB  - ∠3

Subtracting eq (2) from eq (1)

∠ABC  - ∠4 = ∠ACB  - ∠3  (By Euclid's axiom, if If equals be subtracted from equals, the remainders are equal)

Therefore,

∠1  = ∠2

Answer 2

Answer:

angle 4 equal to angle 3 and then angle 4 + angle 1 is equal to angle 3 + angle 2 angle so angle four and three get cancelled angle 1 is equal to angle 2 thus proved