Triangle Similarity: SSS and SAS — Quiz

Question 44 • CMS 2026-2027 Foundations of Math 3 INITIAL CREDIT

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 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 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 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.

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 .

Explanation

The SSS similarity theorem requires all three pairs of corresponding sides to have equal ratios. For triangles UVW and ZXY, compare UV with ZY, WU with ZX, and WV with XY; the three ratios must be equivalent. Choice B states exactly this condition.

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