Two quadrilaterals and are described below

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Two quadrilaterals ABCDABCD and PQRSPQRS are described below. • AB=4 cm,  BC=7 cm,  CD=5 cm,  DA=7 cmAB = 4\,\text{cm},\; BC = 7\,\text{cm},\; CD = 5\,\text{cm},\; DA = 7\,\text{cm} and ∠ABC=110∘,  ∠CDA=110∘.\angle ABC = 110^{\circ},\; \angle CDA = 110^{\circ}. • PQ=4 cm,  QR=7 cm,  RS=5 cm,  SP=7 cmPQ = 4\,\text{cm},\; QR = 7\,\text{cm},\; RS = 5\,\text{cm},\; SP = 7\,\text{cm} and ∠PQR=110∘,  ∠RSP=110∘.\angle PQR = 110^{\circ},\; \angle RSP = 110^{\circ}. Answer the following: (i) Show that the two quadrilaterals are congruent. State a correct correspondence between their vertices. (ii) When the quadrilateral ABCDABCD is cut out from cardboard and placed on PQRSPQRS, which side of ABCDABCD will exactly cover RSRS? Give a reason. (iii) Is knowledge of all the interior angles necessary to decide congruence of these quadrilaterals? Justify your answer briefly.

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