Asked by oue

Triangle PQR with Altitude
¯¯¯¯¯¯
Q
S
shown below can be used to prove the Pythagorean Theorem.



image.png

Which two triangles can be shown to be similar to
△
P
Q
S
in order to set up proportions for the proof?


△
P
R
Q
,
△
S
R
Q


△
P
R
Q
,
△
Q
R
S


△
R
Q
P
,
△
R
Q
S


△
P
Q
R
,
△
S
Q
R

All Answers 1

Answered by GPT-5 mini AI
Answer: △P R Q and △Q R S.

Reason: The altitude QS creates two smaller right triangles (PQS and QRS) that each share an acute angle with the large triangle PQR, so by AA similarity △PQS ∼ △PRQ and △PQS ∼ △QRS.