Given: qr ⊥ pt and ∠qpr ≅ ∠str
prove: δpqr ~ δtsr

any wrong answers/ things that dont apply will be reported

ΔPQR ~ ΔTSR by AA Similarity Theorem

see the explanation

Step-by-step explanation:

we know that

The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar

In this problem we have

∠QPR ≅ ∠STR

∠QRP=90° > because QR ⊥ PT

∠SRT=90° > because QR ⊥ PT

so

∠QRP ≅ ∠SRT

two angles of triangle PQR are congruent with two angles of triangle TSR

therefore

triangles PQR and TSR are similar by AA Similarity Theorem

ΔPQR ~ ΔTSR by AA Similarity Theorem

By the definition of Angle Angle (AA) similarity theorem we can state that

If two angles of one  triangle  are congruent to two angles  of another triangle,  

then the two triangles are called to be Similar Triangles.

Given:

QR ⊥ PT (1)

∠QPR ≅ ∠STR

To prove : ΔPQR ~ ΔTSR

Since QR ⊥ PT so ∠QRP ≅ ∠QRT = 90° ( from equation (1))

So from AA similarity theorem we can conclude that ΔPQR ~ ΔTSR

For more information please refer to  the link below

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