Question

Kelly is completing a proof based on the figure

below.
B
1) AC DF and SAS
BC= EF and SAS
3) ZC ZF and AAS
2)
4)
She was given that ZA = ZEDF, and has already
proven AB DE. Which pair of corresponding
parts and triangle congruency method would not
prove Δ.ΑΒC = _DEF?
E
ZCBA ZFED and ASA

Answer 1

The subject deals with determining an invalid triangle congruence criterion. SSA is generally not accepted, whereas ASA is valid. ASA therefore would not be the criterion that fails to prove congruence between triangles ABC and DEF.

Step-by-step explanation:

The student's question revolves around triangle congruence, specifically looking at why certain parts and methods would not prove the congruence of two triangles ΔABC and ΔDEF. To determine congruence, the student used criteria such as Side-Side-Angle (SSA), which is not a reliable method for proving two triangles are congruent. Instead, criteria such as Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS) are acceptable proofs of congruence.

Knowing that SSA is generally not a valid congruence criterion, it can be concluded that any part of the proof that attempts to establish congruence by using SSA would be incorrect. As for the given choices, ZCBA ≈ ZFED and ASA is indeed a valid congruence rule, and thus, it would not be the pair of corresponding parts and triangle congruency method to prove ΔABC ≠ ΔDEF.

Answer 2

The correct answer would be the last one D