Question

Are the two triangles below similar?

Answer 1

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

$\angle U = 80^{\circ}$

$\angle V= 55^{\circ}$

By angle sum  property of triangle;

$\angle U + \angle V + \angle T = 180^{\circ}$

Substitute the given values;

$80^{\circ}+ 55^{\circ} + \angle T = 180^{\circ}$

$135^{\circ} + \angle T = 180^{\circ}$

⇒$\angle T = 180^{\circ}- 135^{\circ} = 45^{\circ}$

Now, In ΔUTV and ΔYXW

$\angle V = \angle W = 55^{\circ}$

$\angle T = \angle X = 45^{\circ}$

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;

$\triangle UVT \sim \triangle YXW$

Answer 2

Yes they are similar. I believe one of them is smaller and upside. The size is different but the shape is the same!

Hope this helped  :)