Question

Determine whether the triangles are similar, if so what is a similarity statement in the postulate or theorem used?

Answer 1

Answer:

It is the secon option ∆TRS ≈ ∆TPQ ; SAS

Step-by-step explanation: angle t is equal to angle t because it is the same angle

line TR divided by line TP is equal to line TS divided by TQ

Answer 2

Answer:  The correct option is

$(B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.$

Step-by-step explanation:  We are given to check whether the triangles in the figure are similar or not. If so, we are to state the similarity statement.

From the figure, we note that

in the triangles TPQ and TRS, we have

$TP=42,~TQ=28,TR=42+6=48,~~TS=28+4=32.$

Therefore, the ratios of the corresponding sides of two triangles are

$\dfrac{TP}{TR}=\dfrac{42}{48}=\dfrac{7}{8},\\\\\\\dfrac{TQ}{TS}=\dfrac{28}{32}=\dfrac{7}{8}.$

Now, in ΔTPQ and ΔTRS, we have

$\dfrac{TP}{TR}=\dfrac{TQ}{TS},\\\\\\m\angle TPQ=m\angle TRS~~~\textup{[common angle]}$

So, triangles TPQ and TRS are similar by SAS proportionality postulate.

Thus, the correct option is

$(B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.$