Q4 of 49 Page 54

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

In Δ LNP and Δ MNR


LP = MR( Since PQ = QR)


PN = NR(N is a midpoint)


∠LPN = ∠MRN(Base angles of an isosceles triangle)


So Δ LNP and Δ MNR to each other by S.A.S. axiom of congruency


Hence LN = MN (Corresponding parts of Congruent Triangles)


More from this chapter

All 49 →
2

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

 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?


 1

Suppose ABCD is a rectangle. Using the RHS theorem, prove that triangles ABC and ADC are congruent.

 2

Suppose ABC is a triangle and D is the midpoint of BC. Assume that the perpendiculars from D to AB and AC are of equal length. Prove that ABC is isosceles.