Gabylovesyou
  • Gabylovesyou
The figure below shows a square ABCD and an equilateral triangle DPC.
Mathematics
schrodinger
  • schrodinger
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Gabylovesyou
  • Gabylovesyou
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°.
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Gabylovesyou
  • Gabylovesyou
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  • Gabylovesyou

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Gabylovesyou
  • Gabylovesyou
phi
  • phi
Can you rule out any of the statements (because the are true... and we want the false one) ?
Gabylovesyou
  • Gabylovesyou
is the false one B ?
phi
  • phi
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)
Gabylovesyou
  • Gabylovesyou
Well i know D is true so its not that one
Gabylovesyou
  • Gabylovesyou
wait C looks wrong..
phi
  • phi
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.
Gabylovesyou
  • Gabylovesyou
A looks like its right too
phi
  • phi
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.
Gabylovesyou
  • Gabylovesyou
Thank you!
phi
  • phi
yw

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