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Home / Geometry / Prove that the sum of the angles of a quadrilateral is equal to 4 right angles.

# Prove that the sum of the angles of a quadrilateral is equal to 4 right angles.

## Solution:General enunciation: We have to prove that the sum of the angles of a quadrilateral is equal to 4 right angles.

Particular enunciation: Let four angles of a quadrilateral ABCD be ∠A, ∠B, ∠C, and ∠D. We have to prove that sum of the four angles equal to 4 right angles that is ∠A+∠B+∠C+∠D= 4 right angles.

Construction: We join A with C and B with D.

Proof: We know the sum of the three angles of a triangles is equal to two right angles.

From triangle ABC

∠BAC+∠ABC+∠BCA=1800—————————————–(1)

Again from triangle ADC

∠DAC+∠ADC+∠DCA=1800——————————————(2)

Now adding (1) and (2) we have,

∠BAC+∠ABC+∠BCA+∠DAC+∠ADC+∠DCA=3600

⇒(∠BAC+∠DAC)+ ∠ABC+(∠BCA+∠DCA)+ ∠ADC=3600

⇒ ∠BAD+∠A BC+∠BCD+∠ADC=3600

⇒∠A+∠B+∠C+∠D=3600=4 right angles. (Proved)

## If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.

If two triangles have the three sides of the one equal to the three sides ...