Question

△ABC and △RST are similar triangles.

Which of the following must be true?
∠B≅∠S
AB
BC
=
RT
ST
∠C≅∠R
SR
≅
AB
Submit

Answer 1

Only ∠B ≅ ∠S must be true.

Reason: ABC ~ RST matches A↔R, B↔S, C↔T, so corresponding angles are equal: ∠A≅∠R, ∠B≅∠S, ∠C≅∠T. Corresponding sides are proportional: AB/RS = BC/ST = AC/RT.

Thus:
- ∠B≅∠S — true.
- AB/BC = RT/ST — false (AB/BC = RS/ST, not RT/ST).
- ∠C≅∠R — false (∠C≅∠T).
- SR ≅ AB — false in general (sides are proportional, not necessarily equal unless scale factor = 1).