1. Determine if the polygons are similar.

Question

Are the triangles similar (yes or no)? Yes

Hint: theorems we learned to prove two triangles similar include AA, SAS and SSS.

Which theorem can you use to prove the two triangles similar? sas

Work or explanation:

Answer 1

To show that two triangles are similar using SAS (Side-Angle-Side) theorem, we need to prove that:

1. Two pairs of corresponding sides are proportional
2. The included angles between these sides are equal

Let's consider the given triangles and their corresponding sides:

Triangle ABC : AB = 8, AC = 6, BC = 10

Triangle DEF : DE = 4, DF = 3, EF = 5

We can see that AB/DE = AC/DF = BC/EF = 2. This means that the corresponding sides of the triangles are proportional.

Now, we need to show that the included angles are equal. We can see that angle A of triangle ABC is equal to angle D of triangle DEF (they are both right angles). We are also given that angle B of triangle ABC is equal to angle E of triangle DEF.

Therefore, by SAS theorem, the two triangles are similar.

Answer: Yes, the triangles are similar, and we can use SAS theorem to prove it.