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Consider the two given triangles. Are they similar triangles? Use two proportions to support your answer.

Consider the two given triangles. Are they similar triangles? Use two proportions to support your answer.

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Theoretical probability

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Q. Consider the two given triangles. Are they similar triangles? Use two proportions to support your answer.

Identify sides/angles: Step $1$ : Identify corresponding sides and angles of the triangles to set up proportions.
Set up first proportion: Step $2$ : Set up the first proportion using sides $\frac{AB}{DE} = \frac{BC}{EF}$ . Assume $AB = 4\,\text{cm}$ , $DE = 8\,\text{cm}$ , $BC = 6\,\text{cm}$ , $EF = 12\,\text{cm}$ . Calculate $\frac{AB}{DE}$ and $\frac{BC}{EF}$ .
Set up second proportion: Step $3$ : Set up the second proportion using sides $AC/DF$ . Assume $AC = 5\,\text{cm}$ , $DF = 10\,\text{cm}$ . Calculate $AC/DF$ .
Compare results: Step $4$ : Compare the results of the proportions. If all corresponding sides have the same ratio, the triangles are similar.

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