Omari wants to prove △ABC≅△QRS

Question

by the ASA Congruence Theorem. What information is missing that would allow him to use this theorem?

(1 point)
Responses

AB¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯
line segment cap A cap b is congruent to line segment cap q cap r - no response given

∠B≅∠R
∠B≅∠R
- no response given

BC¯¯¯¯¯¯¯¯≅RS¯¯¯¯¯¯¯
line segment cap b cap c is congruent to line segment cap r cap s - incorrect

∠C≅∠S

Answer 1

To use the ASA (Angle-Side-Angle) Congruence Theorem, Omari needs to have two angles and the included side congruent between the two triangles. Based on the information provided:

1. AB ≅ QR - This states that the sides are congruent.
2. ∠B ≅ ∠R - This states that one pair of angles is congruent.
3. BC ≅ RS - This states that another pair of sides is congruent, but it is not the included side for the angle pair given above.
4. ∠C ≅ ∠S - This states that another pair of angles is congruent.

For Omari to prove that △ABC≅△QRS using the ASA theorem, he needs one of the following pairs to be confirmed:

• The angle (∠A) between the sides AB and AC needs to be congruent to the angle between the corresponding sides QR and QS.

Thus, the missing information needed to use the ASA Congruence Theorem is either:

• ∠A ≅ ∠Q (the angle at vertex A must be congruent to the angle at vertex Q) or the confirmation that one of the angles mentioned along with the included side is the correct configuration.

In summary, if Omari has two angles and the included side congruent, then he can proceed with using the ASA congruence theorem. If either ∠A or its corresponding angle ∠Q is not known to be congruent, approval of triangle congruence will be incomplete.

Answer 2

Which triangle congruence criterion would you use to state that the given triangles are congruent? (1 point) Responses SSA SSA ASA ASA AAS AAS SAS SAS