Question

Seth 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.



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

Answer 1

Triangle ADC is similar to triangle BAC by the SAS similarity theorem.
Triangle ADB is similar to triangle CDA by the SAS similarity theorem.

Triangle ADC is similar to triangle BAC by the AA similarity theorem.
Triangle ADB is similar to triangle CDA by the AA similarity theorem.

Answer 2

@Mertsj

Answer 3

@jim_thompson5910

Answer 4

What do you mean by BC2, etc

Answer 5

squared

Answer 6

its the pythagorean theorem i just left out ^

Answer 7

srry

Answer 8

I think the third one. The first two use congruence reasons. and the triangles are certainly no congruent. The fourth one doesn't contain the side BC.

Answer 9

k

Answer 10

the SAS similarity theorem isn't a congruence property, it's a similarity property

Answer 11

therefore....?

Answer 12

I'm just pointing that out to Mertsj

Answer 13

Thanks.

Answer 14

luckily, there are no common sides and none of the sides are known

so you can't rely on any side lengths, which means you're not using the SAS similarity theorem

so that allows you to eliminate choices A and B

Answer 15

but you can prove/show that the corresponding angles are congruent, which will allow you to use the AA similarity theorem

Answer 16

so you agree with mertsj?

Answer 17

@jim_thompson5910

Answer 18

still working it out, one sec

Answer 19

got it?

Answer 20

yeah if you use this drawing, you'll see that you're using triangles 1,3 to create one ratio

then triangles 2,3 to create another ratio

you'll then be able to (with a few more steps) create BC^2 = AB^2 + AC^2

Answer 21

sry this drawing from this link

http://math.nmsu.edu/breakingaway/Lessons/PTUST/PTUST.html

Answer 22

therefore u agree with mertsj?

Answer 23

yep