To determine whether the two triangles are similar, we need to analyze the side lengths of both triangles and check the ratios of the corresponding sides.
Triangle 1 (M-K-L):
- Side MK (left) = 10
- Side KL (bottom) = 20
- Side ML (right) = 15
Triangle 2 (R-P-Q):
- Side RP (left) = 12
- Side PQ (bottom) = 18
- Side RQ (right) = 24
Next, we can calculate the ratios of the corresponding sides:
For Triangle 1:
- \( \text{MK} : \text{KL} : \text{ML} = 10 : 20 : 15 \)
For Triangle 2:
- \( \text{RP} : \text{PQ} : \text{RQ} = 12 : 18 : 24 \)
Now, let's simplify both sets of ratios:
Triangle 1 Ratios:
- MK:KL = \( \frac{10}{20} = \frac{1}{2} \)
- KL:ML = \( \frac{20}{15} = \frac{4}{3} \)
- ML:MK = \( \frac{15}{10} = \frac{3}{2} \)
Triangle 2 Ratios:
- RP:PQ = \( \frac{12}{18} = \frac{2}{3} \)
- PQ:RQ = \( \frac{18}{24} = \frac{3}{4} \)
- RQ:RP = \( \frac{24}{12} = 2 \)
To compare the triangles, we can compute the side length ratios as follows:
- MK : KL : ML = 10 : 20 : 15 = \( 2 : 4 : 3 \) (after reducing)
- RP : PQ : RQ = 12 : 18 : 24 = \( 2 : 3 : 4 \) (after reducing)
Now, we can see that the ratios of the sides are not the same.
Conclusion:
Since the ratios are not equivalent, the two triangles are not similar. The side ratios do not maintain a consistent proportionality factor, which is required for similarity by either AA (Angle-Angle) or SSS (Side-Side-Side).
Final Statement:
Triangles M-K-L and R-P-Q are not similar, as their corresponding side ratios (10:20:15 and 12:18:24) do not match proportionally.
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