Question

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

Explanation:

Identify the given side lengths

Using the Similar Triangles and Corresponding Sides Ratio knowledge points

• Small triangle sides: \(4\), \(6\), and \(5\).
• Large triangle sides:
• Left side: \(4 + 8 = 12\)
• Right side: \(6 + 6 = 12\)
• Bottom side: \(12\)

Check ratios of corresponding sides

Using the Corresponding Sides Ratio knowledge point

• Compare small triangle sides \((4, 5, 6)\) to large triangle sides \((12, 12, 12)\):

$$ \frac{4}{12} = \frac{1}{3} $$

$$ \frac{6}{12} = \frac{1}{2} $$

$$ \frac{5}{12} \approx 0.417 $$

• The ratios of the corresponding sides are not equal.

Evaluate similarity criteria

Using the Similar Triangles knowledge point

• Since the ratios of all three pairs of corresponding sides are not equal, SSS similarity does not hold.
• The shared top angle is included between sides of length \(4\) and \(6\) in the small triangle, and sides of length \(12\) and \(12\) in the large triangle.
• The ratios of these including sides are \(\frac{4}{12} = \frac{1}{3}\) and \(\frac{6}{12} = \frac{1}{2}\). Since \(\frac{1}{3}

eq \frac{1}{2}\), SAS similarity does not hold.

• There is no information to establish AA similarity.
• Therefore, the triangles are not similar.

Answer:

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