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The map given below shows five different villages. Village M lies exactly halfway between the two pairs of villages A and B as well as and P and Q.

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The map given below shows five different villages. Village M lies exactly halfway between the two pairs of villages A and B as well as and P and Q. What is the distance between village A and village P. (Hint: check if ΔPAM ≅ ΔQBM)

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Given that 

AM = MB 

PM = MQ 

also ∠PMA = ∠QMB 

∴ By S.A.S 

ΔPMA ≅ ΔQMB 

Now PA = BQ 

(∵ Corresponding parts of congruent triangles are equal) 

∴ PA = 4 km

i.e., Distance between the villages A and P is 4 km.

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