Question

"Name the postulate or theorem you can use to prove triangle SUR=TVR

Answer 1

SAS Postulate, as that is what SUR and TVR give. 

Answer 2

Answer with explanation:

In Δ S RT and Δ V RU

ST ║ UV

→ ∠U RV = ∠S RT⇒Vertically opposite angles

→∠RST=∠RVU→→Alternate interior angles as, ST ║ UV.

Also, ∠RU V=∠ R T S→→Alternate interior angles as, ST ║ UV.

Δ S RT ~ Δ V RU⇒[AAA]

When triangles are similar their sides are proportional.

$\frac{SR}{RV}=\frac{TR}{RU}$

In Δ S RU and ΔTR V

∠ S RU = ∠TR V⇒Vertically opposite angles

$\frac{SR}{RV}=\frac{TR}{RU}$

≡ Δ S RU ~ ΔTR V→→[S A S]

So,  ΔS UR=ΔT V R , by SAS postulate

Option B