Answer:
Yes, the two similar triangles because there are two pairs of congruent corresponding angles
Step-by-step explanation:
from the give figure:
In ΔUTV
[tex]\angle U = 80^{\circ}[/tex]
[tex]\angle V= 55^{\circ}[/tex]
By angle sum property of triangle;
[tex]\angle U + \angle V + \angle T = 180^{\circ}[/tex]
Substitute the given values;
[tex]80^{\circ}+ 55^{\circ} + \angle T = 180^{\circ}[/tex]
[tex]135^{\circ} + \angle T = 180^{\circ}[/tex]
⇒[tex]\angle T = 180^{\circ}- 135^{\circ} = 45^{\circ}[/tex]
Now, In ΔUTV and ΔYXW
[tex]\angle V = \angle W = 55^{\circ}[/tex]
[tex]\angle T = \angle X = 45^{\circ}[/tex]
AA similarity postulate states that the two triangles are similar if they have two corresponding angles that are congruent or equal in measure.
so, by AA similarity;
[tex]\triangle UVT \sim \triangle YXW[/tex]
