Answer:
VU=UT
Step-by-step explanation:
UY || TX
∠VUY = ∠UTW (corresponding angles )
∠VYU = ∠VXT (corresponding angles ) ----------------------------1
UW || XY
∠UWT = ∠VXT (corresponding angles ) --------------------------2
Form 1 and 2
∠VYU =∠UWT
Theorem : If two of the angles of two triangles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°
Since ∠VUY = ∠UTW and ∠VYU =∠UWT
So, ∠UVY=∠TUW
Now ∠VUY = ∠UTW and ∠VYU =∠UWT and ∠UVY=∠TUW
So, ΔVUY≅ΔUTW (By AAA congruence)
Since the congruent part of congruent triangles are equal .
So, VU=UT
