The figure below shows a square ABCD and an equilateral triangle DPC. Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC. What is the error in Ted’s proof?
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ok the angel ADP=BCP=30 No =60
I think the 3rd line is close but still wrong. the angles inside the equilateral triangle are 60 but the angles he picked out are 90-60= 30 not 60
all other is true
I never really understood proofs..... :(
|dw:1357766947082:dw| a+c=b+d=90 a=b=60 => c=d=30
So if the 3rd one is wrong, then which answer is it?
for example if you have x=(2+2)/2 you know answer is 2 but you can eliminate as below |dw:1357767118129:dw| so the answer is true but proof is false
for these kinds of proofs, showing 2 triangles are congruent, you use one of the standard approaches: SSS, SAS, or ASA knowing that the sides of the triangles are part of a square and an equilateral triangle should be a clue to use SAS (you know 2 sides) or maybe SSS. to use SAS you need to show the angle between the sides are = for this last bit, use the fact that the angles in a square are 90 the angles in an equilateral triangle are 60 can you see how to figure out angle ADP ?
Like, if it's 60, then how do we solve the rest?
@phi I don't understand...
you must just proof that the angel ADP=BCP=30 No =60 and it is very easy because 1- every angel on equilateral triangle are equal , and we know sum of angels of triangle is 180, so each angel in equilateral triangle is equal to 60 2-every angel in square are 90, so 90=ADP+PDC=ADP+60 so ADP=30 3- as follow PCB=30 (90-60=30) 4- so Proof is complet