Question

Can anyone help me with a geometry question? Medal/Fan Rewarded! :)

Answer 1

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

Nick makes the chart shown below to prove that triangle APD is congruent to triangle BPC:
Statements
1. In triangles APD and BPC; AP = PB
2. In triangles APD and BPC; AD = BC
3. In triangles APD and BPC;angle ADP=angle BCP
4. Triangles APD and BPC are congruent
Justifications
1. P is the vertex of the equilateral triangle
2. Sides of square ABCD are equal
3. Angle ADC = angle BCD = 90° and angle ADP = angle BCP = 90° - 60° = 30°
4. SAS postulate

What is the error in Nick's proof?

He uses the SAS postulate instead of AAS postulate to prove the triangles congruent.

He assumes that AP = PB because P is the vertex of the equilateral triangle.

He uses the SAS postulate instead of SSS postulate to prove the triangles congruent.

He writes the measure of angles ADP and BCP as 30° instead of 45°.