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प्रश्न
In the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.
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उत्तर
In ΔADE and ΔBAC
AE = AC
AB = AD
∠BAD = ∠EAC
∠DAC = ∠DAC = DAC ...(common)
⇒ ∠BAC = ∠EAD = EAD
Therefore, ΔADE ≅ ΔBAC ...(SAS criteria)
Hence, BC = DE.
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संबंधित प्रश्न
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From the information shown in the figure,
In ΔABC and ΔPQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB ≅ ∠PRQ
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∴ ∠BAC ≅ `square` ...corresponding angles of congruent triangles.
`{:("seg AB" ≅ square),("and" square ≅ "seg PR"):}}` ...corresponding sides of congruent triangles
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In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
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(i) ∆ ACB ≅ ∆ ECD
(ii) AB = ED
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