Unsure how to solve: a square ABCD and an equilateral triangle DPC

dannywmarino

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The figure below shows a square ABCD and an equilateral triangle DPC:

image0014e8c69c2.jpg


Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC:
StatementsJustifications
In triangles APD and BPC; DP = PCSides of equilateral triangle DPC are equal
In triangles APD and BPC; AD = BCSides of square ABCD are equal
Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 30°
Triangles APD and BPC are congruentSAS postulate


Which of the following completes Ted's proof?
In square ABCD; angle ADC = angle BCD In square ABCD; angle ADP = angle BCP In triangles APD and BPC; angle ADC = angle BCD In triangles APD and BPC; angle ADP = angle BCP
 
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The figure below shows a square ABCD and an equilateral triangle DPC:

image0014e8c69c2.jpg


Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC:
StatementsJustifications
In triangles APD and BPC; DP = PCSides of equilateral triangle DPC are equal
In triangles APD and BPC; AD = BCSides of square ABCD are equal
Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 30°
Triangles APD and BPC are congruentSAS postulate


Which of the following completes Ted's proof?
In square ABCD; angle ADC = angle BCD
In square ABCD; angle ADP = angle BCP
In triangles APD and BPC; angle ADC = angle BCD
In triangles APD and BPC; angle ADP = angle BCP

What are your thoughts?

Which of those can be concluded from the justification given in the third line, and also lays the foundation for the fourth line?
 
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