triangle a side one 8 side two 10 side three 15 triangle b 12,8 16 24

Question

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Question
Determine if the triangles are similar. If so, state the reason. (7 points)
Responses

AA~
AA~

SAS~
SAS~

SSS~
SSS~

Not similar
Not similar
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Answer 1

To determine if the two triangles (Triangle A and Triangle B) are similar, we can use the criteria for triangle similarity: AA (Angle-Angle), SAS (Side-Angle-Side), or SSS (Side-Side-Side).

For Triangle A:

• Side 1 = 8
• Side 2 = 10
• Side 3 = 15

For Triangle B:

• Side 1 = 12
• Side 2 = 16
• Side 3 = 24

Step 1: Calculate the ratios of corresponding sides.

For Triangle A:

• \( a = 8 \)
• \( b = 10 \)
• \( c = 15 \)

For Triangle B:

• \( a' = 12 \)
• \( b' = 16 \)
• \( c' = 24 \)

Now, calculate the ratios of corresponding sides:

• \( \frac{8}{12} = \frac{2}{3} \)
• \( \frac{10}{16} = \frac{5}{8} \)
• \( \frac{15}{24} = \frac{5}{8} \)

Step 2: Check if the ratios are equal.

The ratios of the corresponding sides are:

• \( \frac{2}{3} \)
• \( \frac{5}{8} \)
• \( \frac{5}{8} \)

Since the ratios \( \frac{2}{3} \) and \( \frac{5}{8} \) are not equal, the triangles do not have proportional sides.

Conclusion:

The triangles are not similar based on the SSS similarity criterion as the ratios of the corresponding sides are not equal. Thus, the response is:

Not similar.