Question

Consider the given figure. Two right angled triangles R T S, and U T S with their hypotenuse side intersecting at the point Q. The opposite side of both triangle have the same length. Using the SSS congruence criterion, what additional information is needed to show that ΔRST ≅ ΔUTS? A. RT ≅ US B. ∠S ≅ ∠T C. RQ ≅ QS D. ∠R ≅ ∠U\

Answer 1

Two or more triangles are said to be congruent if their length of sides and measure of angles are equal. Thus, the required proof expected in the question is option D. <R ≅ <U

When the length of sides or measure of angles of two or more figures is equal, then we say the figures are congruent.

From the given question, the following can be deduced:

RT ≅ US (given: opposite sides are equal)

and TS is a common side for the two triangles.

<TRS  ≅  <RSU (alternate angle property)

<RTS  ≅ <UST (right angle property)

<RTU  ≅  <SUT (alternate angle property)

Therefore it can be observed that the necessary condition to prove that ΔRST ≅ ΔUTS is option D. <R  ≅ <U.

For more clarifications on  ≅ congruent properties of triangles, visit: brainly.com/question/1619927

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