Ken makes a plan before writing a proof to show that the opposite angles of the quadrilateral are congruent. What is missing from his plan?
ΔPQR ≅ ΔRSP by AAA
PS ≅ RQ
PS ≅ RQ
ΔPQR ≅ ΔRSP by SSS
ΔPQR ≅ ΔRSP by ASA
ΔPQR ≅ ΔRSP by SAS
What is missing from Ken’s plan to show that the opposite angles of the quadrilateral are congruent?
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In Ken’s plan, he needs to specify the congruence criteria that will be applicable to prove the congruence of triangles ΔPQR and ΔRSP. While he mentions congruence criteria such as SSS (Side-Side-Side), ASA (Angle-Side-Angle), SAS (Side-Angle-Side), and AAA (Angle-Angle-Angle), he does not provide enough information regarding the actual sides or angles that are being compared.
To complete his plan, Ken should identify which sides or angles of triangles ΔPQR and ΔRSP are congruent using established properties of the quadrilateral (for example, showing that PS and RQ are opposite sides that are equal if it’s a parallelogram) to establish the correct congruence criterion.
In summary, what is missing from his plan is the identification of which congruence criterion applies based on the angles and sides of the quadrilaterals and how those congruences lead to the conclusion that opposite angles are congruent.
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