Question

Triangle upper O upper P upper Q is labeled clockwise starting with vertex upper O in the lower left. Triangle upper R upper S upper T is labeled clockwise starting at vertex upper R in the upper right. Side upper O upper P and side upper R upper S are marked with single congruent tick marks. Side upper P upper Q and side upper S upper T are marked with double congruent tick marks.
What additional piece of information is needed in order to state that △OPQ≅△RST
△
𝑂
𝑃
𝑄
≅
△
𝑅
𝑆
𝑇
by the SSS Congruence Theorem?

(1 point)
Responses

PQ¯¯¯¯¯¯¯¯≅RT¯¯¯¯¯¯¯
𝑃
𝑄
¯
≅
𝑅
𝑇
¯
Modifying above upper P upper Q with bar congruent to Modifying above upper R upper T with bar

OP¯¯¯¯¯¯¯¯≅RT¯¯¯¯¯¯¯
𝑂
𝑃
¯
≅
𝑅
𝑇
¯
Modifying above upper O upper P with bar congruent to Modifying above upper R upper T with bar

OQ¯¯¯¯¯¯¯¯≅RS¯¯¯¯¯¯¯
𝑂
𝑄
¯
≅
𝑅
𝑆
¯
Modifying above upper O upper Q with bar congruent to Modifying above upper R upper S with bar

QO¯¯¯¯¯¯¯¯≅TR¯¯¯¯¯¯¯

Answer 1

You need OQ ≅ RT (same as QO ≅ TR). SSS requires all three corresponding sides to be congruent; OP ≅ RS and PQ ≅ ST are given, so the third pair OQ and RT must be congruent.