Question

Are these triangles similar? If they are similar, mark all the possible similarity theorem(s) to rpove the triangles similar? Mark ALL that apply.A. AA similarity theoremB. SAS similarity theoremC. SSS similarity theoremD. None of the above

Answer 1

Yes, they are similar triangles.

The AA and SAS Similarity Theorems apply.

Step-by-step explanation:

Two triangles can only be similar if they obey any of the below theorems;

*AA Similarity Theorem: If the two triangles have two corresponding angles that are equal. Looking at the given triangles, we can see that angle OVU and angle OWX are congruent(alternate angles). Also angles OXW and OUV are congruent (alternate angles). Since we know these two triangles have two corresponding angles that are congruent, then they

SAS Similarity Theorem: If the ratio of two pairs of corresponding sides of the triangles are equal and their included angles are equal.

Let's go ahead and determine if the given triangles obey this theorem;

`\begin{gathered} (15)/(20)=(6)/(8) \\ \rightarrow(3)/(4)=(3)/(4) \end{gathered}`

We can see that the two corresponding sides of the two triangles have the same ratio, also angle WOX is congruent with angle UOV ( vertically opposite angles), therefore the triangle is similar and obeys this theorem.

SSS Similarity Theorem: If three corresponding sides of the two triangles are in the same ratio.

We're not given the lengths of UV and WX, so we can't tell if this theorem applies.