Question

select the reason why these triangles are similar. if they are not, select
ot similar.\
aa
not similar
sas
sss

Explanation:

Identify the shared angle

Using the Similar Triangles knowledge point
The small triangle and the large triangle share a common angle at the rightmost vertex. Let this shared angle be \(\theta\).

Determine the side lengths of both triangles

Using the Corresponding Sides Ratio knowledge point
For the small triangle, the side lengths adjacent to the shared angle \(\theta\) are:

$$ s_1 = 4,\quad s_2 = 3 $$

For the large triangle, the total side lengths adjacent to the shared angle \(\theta\) are:

$$ L_1 = 12 + 4 = 16,\quad L_2 = 9 + 3 = 12 $$

Compare the ratios of corresponding sides

Using the Corresponding Sides Ratio knowledge point
We check if the ratios of the corresponding adjacent sides are equal:

$$ \frac{L_1}{s_1} = \frac{16}{4} = 4 $$

$$ \frac{L_2}{s_2} = \frac{12}{3} = 4 $$

Since both ratios equal \(4\), the corresponding sides are proportional.

Apply the similarity theorem

Using the SAS Similarity Theorem knowledge point
Since two pairs of corresponding sides are proportional and their included angle is congruent, the triangles are similar.

Answer:

• AA
• Not similar
• SAS (Correct answer)
• SSS