Q2 of 49 Page 45

In the figure ABCD is a square, M, N, O, and P are the midpoints of sides AB, BC, CD and DA respectively. Identify the congruent triangles.

In Δ APM, Δ BMN, Δ CNO and Δ DOP


AB = BC = CD = DA (Sides of a square)


Since M, N, O, and P are the midpoints of sides AB, BC, CD and DA


⇒ 2AM = 2BN = 2CO = 2DP


⇒ AM = BN = CO = DP …(i)


⇒ 2AP = 2BM = 2CN = 2DO


⇒ AP = BM = CN = DO …(ii)


∠PAM = ∠MBN = ∠NCO = ∠ODP(Angles of a square) …(iii)


So Δ APM ≅ Δ BMN ≅ Δ CNO ≅ Δ DOP by S.A.S. axiom of congruency.


More from this chapter

All 49 →
2

Pair of congruent triangles and incomplete statements related to them are given below. Observe the figures carefully and fill up the blanks:

In the adjoining figure, if AC = CE and ΔABC ≅ ΔDEC, then ∠D = _______ and ∠A = _______.


 1

In the adjoining figure, PQRS is a rectangle. Identify the congruent triangles formed by the diagonals.

 3

In a triangle ABC, AB = AC. Points E on AB and D on AC are such that AE = AD. Prove that triangles BCD and CBE are congruent.

 4

In the adjoining figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that DE || BC. [ hint:-use the concept of alternate angles.]