Question

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➡ Prove the angle sum property of triangle.

Detailed answers required.

Answer 1

Hey there !!


Prove the angle sum property of triangle.


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1st method .

→ Based on alternate interior angles property.


2nd method.


→ Based on the theorem that the exterior angle of a triangle is equal to the sum of its two opposite angles.


3rd method.

→ Based on theorem that the sum of all exterior angle of a polygon is 360° .


✔✔ Hence, it is proved ✅✅.

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#BeBrainly.

Answer 2

$\huge \bold {\mathfrak {hey}}$

✔️ $\underline \bold {Diagram \: In \: Pic}$

Let us see what is given in the statement about that is a hypothesis and what we need to prove we are given a triangle PQR and < 1, <2 and < 3 are the angles of triangle PQR see in figure.

We need to prove that <1 + <2 + <3 = 180°. Let us draw a line XPY parallel to QR through the opposite vertex P, as shown in figure. so that we can use the properties related to parallel lines.

Now,

XPY is a line

Therefore, <4 + <1 + <5 = 180° - - - - -(1)

But XPY II QR and PQ, PR are transversal.

So,

<4 = <2 and <5 = <3 ( Alternate angles)

Substituting <4 and <5 in (1) we get,

<2 + <1 + <3 = 180°

That is,

<1 + <2 + <3 = 180°

$\huge {\boxed {Hence, \: Proved}}$



➡️ Hope it will help you

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