L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD, prove that DL, DK, BM and BN enclose a rhombus
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Pic have the solution......
Hope it helps..... with diagram
Hope it helps..... with diagram
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Proved below.
Step-by-step explanation:
Given:
Here, L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD.
Construction:
Join BN, DL, KD, BM.
Proof:
As shown in the figure below, L, M, N, K are mid-points,
⇒ BN║DL and BQ║DK
Therefore DNBQ is a parallelogram.
⇒Δ ABN ≅ Δ ADK [SAS = SAS congruency]
⇒ ∠ ABN = ∠ ADK [By CPCT] [1]
Also, Δ PND ≅ Δ PKB [ASA congruency]
Therefore PB = PD [By CPCT] [2]
So DQBP is a rhombus [ from 1 and 2 ]
Hence DL, DK, BM and BN enclose a rhombus.
Hence proved.
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