consider the diagram. which congruence theorem can be used to prove △abr≅△rca? hl sss asa sas

consider the diagram. which congruence theorem can be used to prove △abr≅△rca? hl sss asa sas

consider the diagram. which congruence theorem can be used to prove △abr≅△rca? hl sss asa sas

Answer

Brief Explanations:

  1. Analyze congruence theorem conditions:
    • HL (Hypotenuse - Leg) is for right - triangles where hypotenuse and one leg are equal. There's no indication of hypotenuse - leg equality here.
    • SSS (Side - Side - Side) requires all three sides of one triangle to be equal to the corresponding three sides of the other triangle. No information about all three sides being equal is given.
    • ASA (Angle - Side - Angle) requires two angles and the included side to be equal. There's no such information.
    • In parallelogram (ABCD) (assuming it's a parallelogram from the context of the diagram), (AB = RC) (opposite sides of a parallelogram), (\angle B = \angle C) (opposite angles of a parallelogram), and (BR=CA) (opposite sides of a parallelogram). So, by SAS (Side - Angle - Side) congruence theorem, (\triangle ABR\cong\triangle RCA) as we have two sides and the included angle equal.

Answer:

SAS