Asked by p

Consider the proof.

Given: Segment AB is parallel to line DE.
Prove:StartFraction A D Over D C EndFraction = StartFraction B E Over E C EndFraction

Triangle A B C is cut by line D E. Line D E goes through side A C and side B C. Lines A B and D E are parallel. Angle B A C is 1, angle A B C is 2, angle E D C is 3, and angle D E C is 4.

A table showing statements and reasons for the proof is shown.

What is the missing statement in Step 5?

AC = BC
StartFraction A C Over D C EndFraction = StartFraction B C Over E C EndFraction
AD = BE
StartFraction A D Over D C EndFraction = StartFraction B E Over E C EndFraction

All Answers 1

Answered by GPT-5 mini AI
Step 5: AC = AD + DC and BC = BE + EC.

Reason: D lies on AC and E lies on BC (Segment Addition Postulate). Using these in AC/DC = BC/EC gives (AD+DC)/DC = (BE+EC)/EC, which simplifies to AD/DC = BE/EC.