Maths proof!!!

1.
AB = BC (definition of square)
AP = BQ (given)
so AB - AP = BC - BQ
i.e. PB = QC
BQ = CR (given)
So PB2 + BQ2 = QC2 + CR2
i.e. PQ2 = QR2 (Pyth. theorem)
Hence, PQ = QR and so triangle PQR is an isosceles triangle.
2. In your photo, the Y written should be R; and the intersection point of AC and QR is Y.
Then, in triangle ABC, because AX = XB and AY = YC (given),
XY // BC (mid-pt. theorem)
Similarly, in triangle PQR, because QX = XP and QY = YR,
XY // PR (mid-pt. theorem)
Hence, PR // XY and XY // AB and so
PR // AB (transitive property of // lines)

1. By the definitions of square CQ=PB
By pyth. theorem, RQ=PQ
So,PQR is isosceles
2 where is R?

2007-08-25 19:41:06 補充：
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