Question

write the angle sum property of a triangle and prove it

Answer 1

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Answer 2

Answer:

$\maltese\underline{\textsf{\textbf{AnsWer :}}}\:\maltese✠$

Angle sum property

The sum of the interior angles of a triangle is 180⁰

Proof

$\red{ \bold{to \: prove}} \\ \angle1 + \angle2 + \angle3 = 180 \degree$

Construction:

Draw DE || BC through A

$\angle4 = \angle2 \\ \angle5 = \angle3$

(angle 4,2 and angle 5,3 are alternate interior angles)

$\implies \: \angle1 + \angle2 + \angle3 = \angle4 + \angle5 + \angle6$

$\angle4 + \angle5 + \angle6 = 180 \degree$

(Because angles 4,5 and 6 are on a straight line)

$\tt{\bold{ \red{hence \: proved}}}$