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

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12

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13

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14

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15

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