Question

9. Determine if triangle LMN and triangle OPQ are or are not similar, and, if they are, state how you know.

Answer 1

The triangle LMN and OPQ are similar

Explanation:

If we rotate the smaller triangle a bit, we can see that their sides share scale factors. The scale factor is 3. (24 x 3 = 72), (23 x 3 = 69), (18 x 3 = 54).

Hence, this shows they are similar cause all the sides share a scale factor of 3.

Answer 2

are

Explanation:

You want to know if ∆LMN is similar to ∆OPQ given their side lengths:

• LM = 23, MN = 24, NL = 18
• OP = 69, PQ = 72, QO = 54

Corresponding sides

The ratios of corresponding side lengths are ...

OP/LM = 69/23 = 3

PQ/MN = 72/24 = 3

QO/NL = 54/18 = 3

Corresponding side lengths are proportional, so the triangles are similar.

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Additional comment

As is often the case when a geometrical figure is over-specified, the given dimensions are inconsistent. The angle shown is closer to 70°.