i want all the solution of these theorems aas soon as possible

1.prove that sum of three angles of a triangle is 180 degree

2.Angle opposite to equal sides of a triangle are equal

3.Two triangles are congurent,if any two angles and included side of one triangle is equal to any two angles and the included side of the other triangle.

4.If two lines intersect at each other at point o.Prove that they are vertically opposite angles.

Hi!

Assuming you want the answer for the theorem;

Assuming you want the answer for the theorem;

**Prove that sum of three angles of a triangle is 180 degree**

Here is the answer to your query.

Consider a triangle PQR and ∠1, ∠2 and ∠3 are the angles of Δ PQR (figure shown below). We need to prove that ∠1 + ∠2 + ∠3 = 180°.

The straight lines AB and CD intersect in O.

∴ ∠AOC + ∠AOD = 180° … (1) (Linear pair)

∠AOD + ∠BOD = 180° … (2) (Linear pair)

From (1) and (2), we get

∠AOC + ∠AOD = ∠AOD + ∠BOD

∠AOC = ∠BOD

Similarly, ∠BOC = ∠AOD

Thus, if two straight intersect each other, then the pair of vertically opposite angles are equal.

Cheers!

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