Question

6 finish the triangle proof by dragging the correct reasons to their box. there will be two extra unused reasons! given: ab || de, be bisects ad prove: ab ≅ de ab || de ac = cd be bisects ad ab = de reflexive property cpctc sas ∠acb = ∠dce ∠bac = ∠edc △abc ≅ △dec alternate interior angles given given asa vertical angles definition of bisect

Explanation:

Step1: Write the first two statements and reasons

1. \(AB\parallel DE\) (Reason: Given)
2. \(BE\) bisects \(AD\) (Reason: Given)

Step2: Use the property of parallel lines

Since \(AB\parallel DE\), \(\angle BAC=\angle EDC\) (Reason: Alternate Interior Angles)

Step3: Use the definition of bisect

Since \(BE\) bisects \(AD\), \(AC = CD\) (Reason: Definition of Bisect)

Step4: Use vertical angles

\(\angle ACB=\angle DCE\) (Reason: Vertical Angles)

Step5: Prove triangle congruence

\(\triangle ABC\cong\triangle DEC\) (Reason: \(ASA\))

Step6: Use CPCTC

\(AB\cong DE\) (Reason: \(CPCTC\))

Answer:

Statement	Reason
\(BE\) bisects \(AD\)	Given
\(\angle BAC=\angle EDC\)	Alternate Interior Angles
\(AC = CD\)	Definition of Bisect
\(\angle ACB=\angle DCE\)	Vertical Angles
\(\triangle ABC\cong\triangle DEC\)	\(ASA\)
\(AB\cong DE\)	\(CPCTC\)