Question

a triangle PQR prove that sum of its angle = 180 degree

Answer Fast

Answer 1

$\huge{\bf{\underline{\purple{Answer :}}}}$

$\bold{\red{Angle \ sum \ Property \ of \ triangle :-}}}$

⇒The sum of three angles of a triangle is 180° and this property of triangle is called Angle sum Property of Triangle .

$\rule{200}2$

Given,

• PQR is a triangle

To Prove ,

• ∠P + ∠Q + ∠R = 180°

Construction,

• Extend QR to the point M . At the point R , draw RN || PQ

Proof,

⇒PQ||NR  And PR is transversal

Therefore,

$\implies \bold{\angle QPR = \angle PRN }$................. 1) ( by Alternative interior  angle )

⇒PQ||NR and QM is the transversal .

Therefore,

$\implies \bold{ \angle PQR = \angle NRM}$................. 2) ( by Corresponding Angle)

From the According to Figure Construction  :-

$\implies \bold{\angle PRQ + \angle PRN + \angle NRM = 180^{\circ}}$............(by Linear pair )

Now From first and Second Equation :

$\implies \bold{\angle P + \angle Q + \angle R = 180^{\circ}}$

Hence Proved

$\rule{200}2$

Answer 2

⠀⠀ıllıllı uoᴉʇnloS ıllıllı

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

The sum of the angles of a triangle is 180°.

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Given:

• A triangle PQR.

To prove:

• Prove that sum of its angle = 180 degree

Construction:

• Extend QR to the point M . At the point R , draw RN || PQ

Proof:

• PQ||NR And PR is transversal.

Therefore:

➠ ∠QPR = ∠PRN ..... (i) . [Alternate interior angles]

➠ PQ||NR and QM is the transversal .

Similarly,

➠ ∠PQR = ∠NRM ....... (ii) . [By corresponding angle ]

Now, according to the figure construction:

➠ ∠PQR + ∠PRN + ∠NRM = 180° [By linear pair]

From first and second equation:

• ∠P + ∠Q + ∠R = 180 degree.

Hence, it is proved.

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Additional Information:

What is Triangle?

• Triangle is a closed figure which has three sides, three vertices and three angles.

How many types of triangle?

• On the basis of sides there are three types of triangle:

(1) Scalene

(2) Isosceles

(3) Equilateral

• On the basis of angles there are three types of triangle:

(1) Acute angled

(2) Right angled

(3) Obtuse angled

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$