Question

complete each two - column proof.

1. given: ( kccong ba,akcong cb )

prove: ( \triangle abccong\triangle cka )
statements reasons

Explanation:

Step1: List the given information

Statements: \(KC\cong BA\), \(AK\cong CB\)
Reasons: Given

Step2: Find the common side

Statements: \(AC = AC\)
Reasons: Reflexive Property of Congruence (\(a = a\) for any segment \(a\))

Step3: Apply SSS (Side - Side - Side) congruence criterion

Statements: \(\triangle ABC\cong\triangle CKA\)
Reasons: SSS Congruence Theorem (If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent). Since \(KC\cong BA\), \(AK\cong CB\), and \(AC\cong AC\), by SSS, \(\triangle ABC\cong\triangle CKA\)

Answer:

Statements	Reasons
\(AC = AC\)	Reflexive Property of Congruence
\(\triangle ABC\cong\triangle CKA\)	SSS Congruence Theorem