Q2 of 49 Page 54

In a square PQRS, diagonals bisect each other at O. Prove that ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ΔSOP.

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In ΔPOQ, ΔQOR , ΔROS, and ΔSOP


PQ = QR = RS = SP (All sides of a square are equal)


∠POQ = ∠QOR = ∠ROS = ∠SOP = 900 (Diagonals of a square bisect at right angle)


PO = QO = RO = SO (Diagonals bisect each other)


So ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ΔSOP by S.A.S. axiom of congruency


More from this chapter

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5

Suppose ABC is an equiangular triangle. Prove that it is equilateral.(You have seen earlier that an equilateral triangle is equiangular. Thus for triangles equiangularity is equivalent to equilaterality.)

 1

In a triangle, ABC, AC = AB, and the altitude AD bisect BC. Prove that ΔADC ≅ ΔADB.

 3

In the figure, two sides AB, BC and the median AD of ΔABC are respectively equal to two sides PQ, QR and median PS of ΔPQR. Prove that

(i) ΔADB ≅ ΔPSQ;


(ii) ΔADC ≅ ΔPSR.


Does it follow that triangles ABC and PQR are congruent?


 4

In ΔPQR, PQ = QR; L, M, and N are the midpoints of the sides of PQ, QR and RP respectively. Prove that LN = MN.