Triangle Similarity — Test

Question 9 • CMS 2026-2027 Foundations of Math 3 INITIAL CREDIT

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

Answer

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

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

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

Explanation

For SAS similarity, two pairs of corresponding sides must be proportional, and the angles between those sides must be congruent. In choice C, UV corresponds to XY and WV (the same side as VW) corresponds to ZY, so the ratios compare the two side pairs. The included angles are ∠V and ∠Y, which the choice states are congruent.

AI-written and checked against the verified answer.

More from this Course

Test

Test

Quiz