• Math

  EXPLAIN INTERIOR ANGLE SUM PROPERTY OF A TRIANGLE

  Posted by Suraj on June 22, 2023 at 5:05 pm

  What is the sum of all interior angles of a triangle and explain how ?

  • This discussion was modified 10 months, 1 week ago by  Suraj.

  Nayani replied 10 months, 1 week ago 2 Members · 1 Reply

  • angles
  • sum
  • Triangles
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  Nayani

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  June 22, 2023 at 5:36 pm

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  The sum of all interior angles of a triangle is always 180 degrees. This property holds true for all triangles, regardless of their shape or size.

  Proof of ANGLE SUM PROPERTY THEOREM:

  Step 1: Draw a line AB through the vertex P and parallel to the side QR of a triangle PQR.

  Step 2: ∠APQ + ∠QPR + ∠RPB = 180 degrees

  [Linear Pair theorem] -(1)

  Step 3: ∠APQ = ∠PQR [Alternate interior angles] -(2)

  Step 4: ∠RPB = ∠PRQ [Alternate interior angles] -(3)

  Step 5: Substituting equation (2) and (3) in equation

  Thus, the theorem is proved.

  

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