Right triangle ABC is represented with right angle at vertex B, towards left. Point D lies on side AC. Segment BD is drawn. Angle BDC is marked as right angle.

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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