Question

Prove that sum of all sides of a triangle =180 degree​

Answer 1

$\huge{\mathfrak{\blue{\underline{\underline{SoluTion:-}}}}}$

★ ${\bf{\underline{Given:-}}}$ ABC is a Δ.

★ ${\bf{\underline{To\;Prove:-}}}$ ∠A + ∠B + ∠C = 180°

★ ${\bf{\underline{Construction:-}}}$ Draw a line XY parallel to BC.

★ ${\bf{\underline{Proof:-}}}$

Since XY ║ BC and AC is a transversal, ∠YAC = ∠ACB             [Alternate Interior Angles] ................(1)

Since XY ║ BC and AB is a transversal, ∠XAB = ∠ABC            [Alternate Interior Angles] ................(2)

Now at point A, ∠YAB and ∠XAB from a linear pair. So, ∠YAB + ∠XAB = 180°

⇒ ∠YAC + ∠BAC + ∠XAB = 180°

⇒ ∠ACB + ∠BAC + ∠ABC = 180°

⇒ ∠C + ∠A + ∠B = 180°

⇒ ∠A + ∠B + ∠C = 180°

Hence Proved

Answer 2

Answer:

Step-by-step explanation:

TRIANGLE Proof that the sum of the angles in a triangle is 180 degrees

Theorem. If ABC is a triangle then <)ABC + <)BCA + <)CAB = 180 degrees.

Proof. Draw line a through points A and B. Draw line b through point C and parallel to line a.

Lemma. ...

Proof. ...

Definition.