## Sunshine447 2 years ago 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?

1. Sunshine447

2. Sunshine447

@amistre64

3. Sunshine447

@ParthKohli

4. Sunshine447

@Agent_Sniffles

5. baziham

ok the angel ADP=BCP=30 No =60

6. phi

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

7. baziham

all other is true

8. Sunshine447

I never really understood proofs..... :(

9. baziham

|dw:1357766947082:dw| a+c=b+d=90 a=b=60 => c=d=30

10. Sunshine447

So if the 3rd one is wrong, then which answer is it?

11. baziham

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

12. phi

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 ?

13. Sunshine447

Like, if it's 60, then how do we solve the rest?

14. Sunshine447

@phi I don't understand...

15. baziham

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

16. baziham

ok?

17. Sunshine447

Thanks!

18. baziham