01. Prove that sum of angles of a triangle is 180 degree
Answers
Answer:
it's simple man
Step-by-step explanation:
In the given triangle, ∆ABC, AB, BC, and CA represent three sides. A, B and C are the three vertices and ∠ABC, ∠BCA and ∠CAB are three interior angles of ∆ABC.
Angle Sum Property of a triangle
Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Proof:
Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ←→ parallel to the side BC of the given triangle.
Angle sum property of a triangle theorem 1
Since PQ is a straight line, it can be concluded that:
∠PAB + ∠BAC + ∠QAC = 180° ………(1)
Since PQ||BC and AB, AC are transversals,
Therefore, ∠QAC = ∠ACB (a pair of alternate angle)
Also, ∠PAB = ∠CBA (a pair of alternate angle)
Substituting the value of ∠QAC and∠PAB in equation (1),
∠ACB + ∠BAC + ∠CBA= 180°
Thus, the sum of the interior angles of a triangle is 180°.
Answer:
Hence, the sum of all angles of triangle is 180°.