Question

Zoe is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90o and segment AD is perpendicular to segment BC.

the figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Triangle ADC is similar to triangle ADB by the AA Similarity Theorem.

Triangle ABC is similar to triangle DBA by the AA Similarity Theorem.

Triangle ABC is similar to triangle DBA by the SAS Similarity Theorem.

Answer 1

Triangle ABC is similar to triangle DBA by the AA Similarity Theorem.

Answer 2

@JungHyunRan i dont like ur way of telling direct answers

Answer 3

two triangles ABC and DBA have the same angle \( \Large \angle ABC\)
And, Because \(\Large \angle ACB +\angle ABC =90^o\) , \(\Large \angle DAB + \angle ABC =90^o\) \(\Large \Rightarrow \angle ACB =\angle DAB \)
So Triangle ABC is similar to triangle DBA by the AA Similarity Theorem.

Answer 4

Ok thank you