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State what additional information is required in order to know that the triangles are congruent for the reason given.



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To determine the additional information needed to establish the congruence of triangles based on a given reason (like SAS, SSS, ASA, AAS, or HL), I will need more context about the conditions of the triangles you are referring to. Here are some examples of the types of responses you might need based on the congruence criteria:

  1. If SAS (Side-Angle-Side) is the reason given: You need to know the length of at least one more side to confirm that the triangles are congruent, or the angle must be included between the other two sides.

  2. If SSS (Side-Side-Side) is the reason given: You need the lengths of all three sides of one triangle, and all three sides of the other triangle.

  3. If ASA (Angle-Side-Angle) is the reason given: You need the measure of at least one more angle or the length of the side that is between the two angles already given.

  4. If AAS (Angle-Angle-Side) is the reason given: You will need the measure of one additional angle or the length of the side opposite one of the given angles.

  5. If HL (Hypotenuse-Leg) is the reason given: You need to confirm the length of the leg one triangle shares with the hypotenuse.

Please provide the specific condition or reasoning you are working with so I can assist you appropriately!