Question

There are two triangles, triangle abc and triangle def. side ab is congruent to side de, side bc is congruent to side ef. angle cab is congruent to angle fde. What additional information is needed to show that Δabc ≅ Δdef by sss?

1) ab¯¯¯¯¯¯¯¯≅de¯¯¯¯¯¯¯¯
2) bc¯¯¯¯¯¯¯¯≅ef¯¯¯¯¯¯¯¯
3) ab¯¯¯¯¯¯¯¯≅ac¯¯¯¯¯¯¯¯
4) ac¯¯¯¯¯¯¯¯≅df¯¯¯¯¯¯¯¯

Answer 1

To prove that Δabc ≅ Δdef using SSS, we need to confirm that the third pair of sides, AC and DF, are congruent. This satisfies the criterion of having all three corresponding sides of both triangles congruent.

Step-by-step explanation:

To show that Δabc ≅ Δdef by SSS (Side-Side-Side) congruence theorem, we need three pairs of congruent sides. Since it is given that side AB ≅ DE and side BC ≅ EF, we need to establish the congruence of the third pair of sides to fulfill the SSS criteria.

Therefore, to show Δabc ≅ Δdef by SSS, we need option 4) AC ≅ DF. This is because we require that all three corresponding sides of both triangles are congruent. Having congruent angles alone would not be sufficient under the SSS criterion, as SSS requires the congruence of sides, not angles.