# In the figure x is a point in the interior of square ABCD, AXYZ is also a square. Prove that BX = DZ.

Since ABCD and AXYZ both are squares
∠AZY = ∠AXY
= ∠AXB ... (each 90°) and AX = AZ and AB = AD
∠AZD = ∠AXB ...... (each 90°)
AZ = AX ...... (sides of a square)
AB = AD ...... (sides of a square)
BX = DZ ....... (c.p.c.t.)

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