SOLUTION: given square ABCD, let P and Q be the points outside the square that make triangles CDP and BCQ equilateral. Prove that triangle APQ is also equilateral.
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-> SOLUTION: given square ABCD, let P and Q be the points outside the square that make triangles CDP and BCQ equilateral. Prove that triangle APQ is also equilateral.
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Question 147478: given square ABCD, let P and Q be the points outside the square that make triangles CDP and BCQ equilateral. Prove that triangle APQ is also equilateral. Answer by orca(409) (Show Source):
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To prove triangle APQ is equilateral, we need to show that AP = AQ = PQ.
Next we will show that triangles ABQ, ADP and CPQ are congruent.
< ADP = 90 + 60 = 150
< ABQ = 90 + 60 = 150
< PCQ = 360 - 90 - 60 - 60 = 150
So < ADP = < ABQ = < PCQ
AB = AD = CP
BQ = DP = CQ
So triangles ABQ, ADP and CPQ are congruent.
Thus AP = AQ = PQ
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