1. Given: △ACE, BD⎯⎯⎯⎯⎯∥AE⎯⎯⎯⎯⎯

Prove: BACB=DECD

A triangle with vertices labeled as A, C, and E, and base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2.

Drag an expression or phrase to each box to complete the proof.
Statement Reason
△ACE, BD⎯⎯⎯⎯⎯∥AE⎯⎯⎯⎯⎯ Given
∠4≅∠1, ∠3≅∠2 Response area
Response area Angle-Angle Similarity Postulate
CACB=CECD Definition of similar triangles
CA=CB+BACE=CD+DE Response area
CB+BACB=CD+DECD Substitution Property of Equality
CBCB+BACB=CDCD+DECD Addition of fractions
1+BACB=1+DECD Simplification of fractions
BACB=DECD Subtraction Property of Equality
Corresponding Angles PostulateAlternate Interior Angles PostulateSegment Addition PostulateAC⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯ △ACE∼△BCD

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