Question

Are the two triangles below similar?

Answer 1

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 :)

Answer 2

Yes, the two similar triangles because there are two pairs of congruent corresponding angles

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`