Question

Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and the length of side S T is 16. The length of side T U is 8 and the length of U V is 6.
Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?

StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction

Answer 1

Answers A and B.

Reason: RS/VU = 12/6 = 2 and ST/UT = 16/8 = 2, so RS/VU = ST/UT, and ∠S and ∠U are both right angles (congruent) — this is statement A and gives the SAS similarity. Also RT/VT = 20/10 = 2, so RS/VU = ST/UT = RT/VT (statement B). Statements C and D are false because TU/TS = 8/16 = 1/2, not 2.