Geometry Theorms:-
Today in this article I will show you how to prove theorms releated on triangles and quadrilateral.
1.Prove that sum of three angles of a triangle is 180°.
Answer:- In the picture,
ABC is a Δ , < A ,∠B and∠C are its three angles,
To prove:- < A + < B + <C =180°
Construction:- Through point "A" DE∥ BC is drawn.
Proof:- ∵ In Δ ABC
DE ∥ BC and AB is the transversal,
∴ ∠ B = < DAB [∵ alternate angles are equal].......(1)
Again,
DE ∥ BC and AC is the transversal,
∴ ∠ C = < EAC [ ∵ alternate angles are equal].......(2)
Now (1)+(2) we get,
< B + < C = < DAB + < EAC
again, adding < BAC in both sides of the above equation we get,
<BAC + < B + < C = < DAB +<BAC+<EAC
=> <BAC +<B+<C = <DAE
=> <BAC+<B+<C = 180°[<DAE is a straight angle,so it measures 180°]
∴ <A + <B + <C = 180° Proved
