Question

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

Answer 1

Jake 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; AP = PB Sides of equilateral triangle APB 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 Jake's proof?
He assumes that triangle DPC has all sides equal.

He assumes that triangle APB is an equilateral triangle.

He assumes that the triangles are congruent by the SAS postulate.

He assumes that angle ADC measures 90°.

Answer 2

@ParthKohli

Answer 3

@phi

Answer 4

@hoblos

Answer 5

Can you rule out any of the statements (because the are true... and we want the false one) ?

Answer 6

is the false one B ?

Answer 7

It definitely sounds wrong. they tell us
an equilateral triangle DPC. (which is the big triangle)

If you really want to nail it down, notice that the other statements are true.
(it would be good to see that)

Answer 8

Well i know D is true so its not that one

Answer 9

wait C looks wrong..

Answer 10

I interpret C "generally speaking"
He assumes that the triangles are congruent by the SAS postulate.

in other words, triangles can be proved congruent by using SAS
which is true.

Answer 11

A looks like its right too

Answer 12

They tell you its equilateral, and that means triangle DPC has all sides equal.
(this is testing if you know what equilateral means)

The sad thing is, his two triangles are congruent by SAS
if only he had said side AD= BC (sides of a square are =)

instead he said AP = PB Sides of equilateral triangle APB are equal

they are =, but not because they are parts of an equilateral triangle.

But enough! The answer is B, just like you said.

Answer 13

Thank you!

Answer 14

yw