Question

The figure shows three right triangles. Triangles PQS, QRS, and PRQ are similar.

Theorem: If two triangles are similar, the corresponding sides are in proportion.

Figure shows triangle PQR with right angle at Q. Segment PQ is 4 and segment QR is 9. Point S is on segment PR and angles QSP a

Using the given theorem, which two statements help to prove that if segment PR is x, then x2 = 97?

Segment PR ⋅ segment PS = 16
Segment PR ⋅ segment SR = 36
Segment PR ⋅ segment PS = 36
Segment PR ⋅ segment SR = 81
Segment PR ⋅ segment PS = 16
Segment PR ⋅ segment SR = 81
Segment PR ⋅ segment PS = 81
Segment PR ⋅ segment SR = 16

Answer 1

Figure shows triangle PQR with right angle at Q. Segment PQ is 4 and segment QR is 9. Point S is on segment PR and angles QSP a - suppose you missed from there that angles QSP a - right angle - conform to this posted image

Using the given theorem, which two statements help to prove that if segment PR is x, then x2 = 97?

so this x2 suppose wan be x^2 = 97 ?

so like a first step using Pythagoras theorem you calcule the length of PR

PR = sqrt(81+16)= sqrt97

bc we know that triangle PRQ similar triangle QRS so we can use the proportionality of corresponding sides and write in this way

\[\frac{ PQ }{ PR } = \frac{ QS }{ QR }\]

\[\frac{ 4 }{ \sqrt{97} }= \frac{ QS }{ 9 } => QS = \frac{ 36 }{ \sqrt{97} }\]

Segment PR ⋅ segment PS = 16
Segment PR ⋅ segment SR = 36
Segment PR ⋅ segment PS = 36
Segment PR ⋅ segment SR = 81
Segment PR ⋅ segment PS = 16
Segment PR ⋅ segment SR = 81
Segment PR ⋅ segment PS = 81
Segment PR ⋅ segment SR = 16