Middle School

We appreciate your visit to Which postulate or theorem can be used to prove that A PQR is similar to A PST SSS Similarity Theorem AS Similarity Postulate SAS Similarity. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Which postulate or theorem can be used to

prove that A PQR is similar to A PST?


SSS Similarity Theorem

AS Similarity Postulate

SAS Similarity Theorem

ASA Similarity Theorem

Which postulate or theorem can be used to prove that A PQR is similar to A PST SSS Similarity Theorem AS Similarity Postulate SAS Similarity

Answer :

The triangles PQR and PST can be proven similar using the SAS Similarity Theorem, as they share two proportional sides and an included angle.

To determine which postulate or theorem can be used to prove that triangle PQR is similar to triangle PST, we need to understand the conditions under which triangles are similar.

SAS Similarity Theorem: This states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar. Since we are given two sides and an included angle (angle P) that is common to both triangles, we can use this theorem.

Thus, the correct answer is the SAS Similarity Theorem.

Thanks for taking the time to read Which postulate or theorem can be used to prove that A PQR is similar to A PST SSS Similarity Theorem AS Similarity Postulate SAS Similarity. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Answer:

AA Similarity Postulate

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

step 1

Verify the proportion of the corresponding sides

[tex]\frac{PS}{PQ}=\frac{PT}{PR}[/tex]

substitute

[tex]\frac{45}{20}=\frac{36}{16}[/tex]

[tex]2.25=2.25[/tex] ----> is true

Corresponding sides are proportional

Triangle PQR is similar to Triangle PST

That means

Corresponding angles must be congruent

side QR is parallel side ST

and

[tex]m\angle PQR=m\angle PST[/tex] ----> by corresponding angles

[tex]m\angle PRQ=m\angle PTS[/tex] --> by corresponding angles

so

PQR is similar to PST by AA Similarity Postulate