Question

question 2 of 5 select all the correct answers. which two additional congruencies are necessary to prove that triangles abc and rts are congruent through sas? triangles abc (with angle at b) and rts (with angle at t) are shown. options: sides ab and rt are congruent. angles bac and trs are congruent. sides st and cb are congruent. angles acb and rst are congruent. sides ac and rs are congruent.

Explanation:

To prove \(\triangle ABC \cong \triangle RTS\) by SAS, we need two sides and the included angle. From the triangles, \(\angle B\) and \(\angle T\) are marked (implied congruent). So we need:

1. Sides \(AB\) and \(RT\) (one pair of sides), and
2. Sides \(CB\) and \(ST\) (another pair of sides, as they are adjacent to the congruent angles). Also, angles or sides that align with SAS:

• "Sides \(AB\) and \(RT\) are congruent" (one side)
• "Sides \(ST\) and \(CB\) are congruent" (another side, included with the angle)
• "Angles \(BAC\) and \(TRS\)" – no, not included. "Angles \(ACB\) and \(RST\)" – no. "Sides \(AC\) and \(RS\)" – not included. So the correct ones are "Sides \(AB\) and \(RT\) are congruent" and "Sides \(ST\) and \(CB\) are congruent".

Answer:

• Sides \(AB\) and \(RT\) are congruent
• Sides \(ST\) and \(CB\) are congruent