High School

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 D


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


Statements Justifications

In triangles APD and BPC; DP = PC Sides of equilateral triangle DPC are equal

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° so angle ADP = angle BCP = 60°

Triangles APD and BPC are congruent SAS postulate

What is the error in Ted's proof? (1 point)


He writes the measure of angles ADP and BCP as 60° instead of 45°.

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

He writes the measure of angles ADP and BCP as 60° instead of 30°.

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

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

Answer :

The error in Ted’s proof is that he writes the measure of angles ADP and BCP as 60° instead of 45°.

Here’s why:

In the square ABCD, the diagonals AC and BD intersect at point P, dividing the square into four right triangles. Since the diagonals of a square are equal and bisect each other, AP = BP = CP = DP. Also, since the diagonals of a square are perpendicular bisectors, ∠APD = ∠BPC = 45°, not 60°.

Therefore, the correct statement should be: “Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 45°”.

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