Question

how we easily understand triangles sum

Answer 1

because all know triangle have three sides

Answer 2

(A)By construction:-

1) Draw a triangle on a sheet of paper. Any sort of triangle you like. Use the ruler or straight-edge to ensure the sides are straight:



2) Colour the edges of the triangles. Do not colour the inside of the triangle. If you really want to colour the inside of the triangle, then use a different colour for the inside from the edges:



3) Cut out the triangle. Make sure the edges are as straight as possible:



4) Cut the corners off the triangle. Make the corners large enough so they are easy to handle:



Notice that each corner has two coloured edges and one uncoloured edge. (I should have used a more contrasting colour than green – maybe red – or else pressed harder when I coloured.

5) Draw a straight line on a sheet of paper using the ruler (I used one of the scraps from the paper I cut the triangle out of):



6)Assemble the corners on the straight line. Ensure that (1)coloured edges touch the straight line and (2) coloured edges touch other coloured edges.


(B)By proving:-

Proof:Consider a ∆ABC, as shown in the figure below.To prove the above property of triangles, draw a line
←→
P
Q
parallel to the side BC of the given triangle.


Since PQ is a straight line, it can be concluded that:

∠PAB + ∠BAC + ∠QAC = 180° ………(1)

SincePQ||BCand AB, AC are the transversals,

Therefore, ∠QAC = ∠ACB (pair of alternate angles)

Also, ∠PAB = ∠CBA(pair of alternate angles)

Substituting the value of ∠QAC and∠PAB in equation (1),

∠ACB + ∠BAC + ∠CBA= 180°

Thus, the sum of interior angles of a triangle is 180°.