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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