Question

Which postulate or theorem can be used to

Answer 1

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

$\frac{PS}{PQ}=\frac{PT}{PR}$

substitute

$\frac{45}{20}=\frac{36}{16}$

$2.25=2.25$ ----> 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

$m\angle PQR=m\angle PST$ ----> by corresponding angles

$m\angle PRQ=m\angle PTS$ --> by corresponding angles

so

PQR is similar to PST by AA Similarity Postulate