Mathematics
Use the given figure to prove that, AB = AC.
Triangles
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Answer
From figure,
⇒ AP = AQ (Given)
⇒ ∠BAP = ∠CAQ (Given)
In Δ APQ
⇒ AP = AQ
⇒ ∠AQP = ∠APQ (Angles opposite to equal sides are equal)
⇒ 180° - ∠AQP = 180° - ∠APQ
⇒ ∠AQC = ∠APB (As BPQC is a straight line)
In Δ APB and Δ AQC,
⇒ ∠BAP = ∠CAQ (Given)
⇒ AP = AQ (Given)
⇒ ∠APB = ∠AQC (Proved above)
∴ Δ APB ≅ Δ AQC (By A.S.A. axiom)
We know that,
Corresponding sides of congruent triangles are equal.
∴ AB = AC
Hence, proved that AB = AC.
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In isosceles triangle ABC, sides AB and AC are equal. If point D lies in base BC and point E lies on BC produced (BC being produced through vertex C), prove that :
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Given : ED = EC
Prove : AB + AD > BC.
