Question

What is the error in Nick's proof?

Answer 1

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

ABCD is a square. P is a point inside the square. Straight lines join points A and P, B and P, D and P, and C and P. Triangle DPC is an equilateral triangle

Nick makes the chart shown below to prove that triangle APD is congruent to triangle BPC:

Statements Justifications
In triangles APD and BPC; AP = PB P is the vertex of the equilateral triangle
In triangles APD and BPC; AD = BC Sides of square ABCD are equal
In triangles APD and BPC; angle ADP = angle BCP Angle ADC = angle BCD = 90° and angle ADP = angle BCP = 90° - 60° = 30°
Triangles APD and BPC are congruent 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°.

Answer 2

Hello @nessal and Welcome to OpenStudy! :)

You have posted this question in the OpenStudy Feedback section, I believe you would get much better and faster help if you were to ask your question in the Mathematics section: http://openstudy.com/study#/groups/mathematics