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Question 10 • Mathematics II

How can the triangles be proven similar by the SSS similarity theorem?

Answer

Show that the ratios the fraction with numerator cap u cap v and denominator cap x cap y comma the fraction with numerator cap w cap u and denominator cap z cap x comma ,the fraction with numerator mathrm cap w cap u and denominator mathrm cap z cap x, and the fraction with numerator cap w cap v and denominator cap z cap y are equivalent.

Show that the ratios the fraction with numerator cap u cap v and denominator cap x cap y and the fraction with numerator cap w cap v and denominator cap z cap y are equivalent, and angle cap v is congruent to angle cap y .

Show that the ratios the fraction with numerator cap u cap v and denominator cap z cap y and the fraction with numerator cap w cap u and denominator cap z cap x are equivalent, and angle cap u is congruent to angle cap z .

Show that the ratios the fraction with numerator cap u cap v and denominator cap z cap y , the fraction with numerator cap w cap u and denominator cap z cap x , and the fraction with numerator cap w cap v and denominator cap x cap y are equivalent.

Explanation

The SSS similarity theorem requires all three pairs of corresponding sides to be proportional. For triangles UVW and XYZ, the corresponding sides are UV and XY, UW and XZ, and VW and YZ. Choice B states that the ratios UV/XY, UW/XZ, and VW/YZ are equivalent, which is exactly the required condition. Choices A and D use an angle condition, and choice C mismatches the side correspondences.

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