By comparing the ratios of corresponding sides (AB/DC, BE/CF, AE/DF) and finding them equal (2/7), the SSS Similarity Theorem establishes the similarity of Triangles ABE and DCF.
The Side-Side-Side (SSS) Similarity Theorem is a criterion for proving the similarity of two triangles. According to this theorem, if the corresponding sides of two triangles are in proportion, then the triangles are similar.
In the given image, we have two triangles: Triangle ABE and Triangle DCF. To show that these triangles are similar using the SSS Similarity Theorem, we need to demonstrate that their corresponding sides are proportional.
Let's list the corresponding sides of the two triangles:
Triangle ABE:
Side AB = 10 cm
Side BE = 11 cm
Side AE = 12 cm
Triangle DCF:
Side DC = 35 cm
Side CF = 38.5 cm
Side DF = 42 cm
Now, we need to check whether the ratios of the corresponding sides are equal. Let's compare the ratios:
AB/DC = 10/35
BE/CF = 11/38.5
AE/DF = 12/42
Now, simplify these ratios:
AB/DC = 10/35 = 2/7
BE/CF = 11/38.5 = 2/7 (after multiplying both numerator and denominator by 2)
AE/DF = 12/42 = 2/7 (after dividing both numerator and denominator by 6)
Since all three ratios are equal (all are 2/7), we can conclude that the corresponding sides of the two triangles are proportional. According to the SSS Similarity Theorem, this implies that Triangle ABE is similar to Triangle DCF.
In summary, the SSS Similarity Theorem is applied by comparing the ratios of corresponding sides of the triangles and demonstrating that they are equal, thus proving the similarity of the triangles.
Complete question:
Are the triangles similar? If so, what postulate or theorem proves their similarity?