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19. In the adjoining figure, ABCD is a square of side 2 cm.Sides AB and BC are produced to P and Q respectivelysuch that BP = CQ = 1cm. AQ and DP are joined. IsAQ = DP ? Give reasons.

Answer»

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Yes.AQ= DP

Traingle ABQ and Traingle DAP are congruent with AQ and DP being hypotenuse.

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yes AQ = DP because tiangle ANQ is congruent to triangle DAP

ab=bc( since it is a square)bp=cq (given)

ab+bp=bc+cqap=bq=3 cm

apply pythagorean theory for ADP triangle and ABQ trianglethen AQ=DP=√(2)sq+(3)sq=√13

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BC=AB,So BQ=AP,DA=AB,so by

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both are congruent by RHS

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As , ABQ is congruent to DAP So , AQ=DP Hypotenuses

Triangle AQB Congruent Triangle ADP. (by SAS)

AQ = DP (by CPCT)



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