Tue. Jun 25th, 2024
Fig.1

Let ABC is a triangle whose three angles are ∠A = x°, ∠B = y° and ∠C = z°
We have to prove x° + y° + z° = 180°

Construction : 

Three sides AB, BC, and AC are extended in both the directions. Then a line RAS is drawn from point A in such a way that RAS॥PQ.

Fig.2

Proof:   ∵ RAS॥PQ and MN is transversal ( According to the construction )
∴ ∠CBA = ∠NAS = y°
Similarly, ∠BCA = ∠TAR = z°
Now, at point A, ∠SAC = ∠TAR = z°   ( vertical opposite angles ) and
∠RAB = ∠NAS = y°   ( vertical opposite angles )
Now, At the point A, ∠RAS = 180°            ( straight angle )
⇒ ∠RAB + ∠BAC + ∠SAC = 180°
⇒ y° + x° + z° = 180°
∴  x° + y° + z° = 180° (Proved)

For more details click on the video below.

 

Leave a Reply

Your email address will not be published. Required fields are marked *

Insert math as
Block
Inline
Additional settings
Formula color
Text color
#333333
Type math using LaTeX
Preview
\({}\)
Nothing to preview
Insert
error: Content is protected !!