Question

Make an art integrated assignment of maths Verify the angle sum property of triangle (PLEASE HELP ME IN THIS BY GIVING IDEAS )​ please give me correct answer please please help me I need . IF CORRECT ANSWER I WILL THANK YOU​

Answer 1

Step-by-step explanation:

Theorem 7: The sum of the angles of a triangle is 180o.

Since this is a theorem, let’s try to prove it.

To prove: ∠ 1 + ∠ 2 + ∠ 3 = 180o

Proof:

∠4 = ∠ 3 (Alternate angle theorem) – (i)

∠5 = ∠ 2 (Alternate angle theorem) – (ii)

Now,

∠ 1 + ∠ 4 + ∠ 5 = 180o, Since EF is a line.

Or, ∠ 1 + ∠ 3+ ∠2 = 180o ,Replacing ∠4 with ∠ 3 & ∠5 with ∠ 2 as per eq i & ii.

Exterior Angle of a triangle: Side QR of triangle PQR is produced to point S, ∠ ACD is called an exterior angle of ΔABC

Theorem 8 : If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles

Since this is a theorem, let’s try to prove it.

To prove: ∠9 = ∠ 6 + ∠ 8

Proof:

∠7 + ∠ 6 + ∠ 8 = 180o (Angle Sum property of Triangle) – (i)

∠7 + ∠ 9 = 180o (Linear Pair as BCD is a line) – (ii)

Comparing i & ii , we can say that, ∠9 = ∠ 6 + ∠ 8