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.
3. ∠BCA ≅ ∠DCB Reflexive Property of Congruence
4. ABC ≅ BDC A criterion for similarity
5. BC/DC ≅ AC/BC 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. ABC ≅ ADB AA criterion for similarity
10. AB/AD ≅ AC/AB Corresponding sides of similar triangles are proportional.
11.
12.
13.
14.
15.

CHOICES:
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