prove that the sum of two sides of a triangle is greater than the third side
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Theorem : The sum of two sides of a triangle is greater than the third side
Let PQR is a triangle.
We have to prove that : QP + PR > QR
Proof:
Extend QP to A,
Such that, PA = PR
⇒ ∠ PAR = ∠ PRA
Since, By the diagram,
∠ ARQ > ∠ PRA
⇒ ∠ ARQ > ∠ PAR
⇒ QA > PQ ( Because, the sides opposite to larger angle is larger and the sides opposite to smaller angle is smaller )
⇒ QP + PA > QR
⇒ QP + PR > QR.
Hence, prove,
Note: similarly we can proved, QP + QR > PR or PR + QR > QP
Thus, The sum of two sides of a triangle is greater than the third side
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hence proved that sum of Two sides of a triangle
Step-by-step explanation:
is always greater than the third side
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