Drag the tiles to the correct boxes to complete the pairs. The figure shows ∆ABC with m∠ABC = 90°. The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. Match the remaining steps to their correct sequence in the proof. Statement Reason 1. Draw . construction 2. ∠ABC ≅ ∠BDC Angles with the same measure are congruent. 4. ∠BCA ≅ ∠DCB Reflexive Property of Congruence 4. AA criterion for similarity 5. Corresponding sides of similar triangles are proportional. 6. BC2 = AC × DC cross multiplication 7. ∠ABC ≅ ∠ADB Angles with the same measure are congruent. 8. ∠BAC ≅ ∠DAB Reflexive Property of Congruence 9. AA criterion for similarity 10. Corresponding sides of similar triangles are proportional. 11. 12. 13. 14. 15. AB2 + BC2 = AC2 Reason: multiplication AB2 + BC2 = AC × AC Reason: segment addition AB2 = AC × AD Reason: cross multiplication AB2 + BC2 = AC(AD + DC) Reason: Distributive Property AB2 + BC2 = AC × AD + AC × DC Reason: addition 11 arrowBoth 12 arrowBoth 13 arrowBoth 14 arrowBoth 15 arrowBoth