What is the missing statement in the proof? scroll down to see the entire proof. ∠bdc≅∠adb ∠bca≅∠dcb ∠bac≅∠bad ∠dbc≅∠bac done given: δabc with m∠abc = 90° (view diagram) prove: ab2 + bc2 = ac2 statement reason 1. draw bd¯¯¯¯¯⊥ac¯¯¯¯¯ (view diagram). construction 2. ∠abc≅∠bdc angles with the same measure are congruent. 3. reflexive property of congruence 4. δabc~δbdc aa criterion for similarity 5. bcdc=acbc 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. δabc~δadb aa criterion for similarity 10.abad=acab corresponding sides of similar triangles are proportional. 11. ab2 = ac × ad cross multiplication 12. ab2 + bc2 = ac × ad + ac × dc addition 13. ab2 + bc2 = ac(ad + dc)

Answer with explanation:

In ΔABC, Right Angled at B.

Draw , B D ⊥ AC

Also,1. ∠B DC≅∠A DB

2.∠B CA≅∠DCB

3.∠B AC≅∠BAD

4.∠D BC≅∠B AC

To Prove: →AB²+BC²=AC²

Solution:

In ΔABC and ΔB DC

B D ⊥ AC→→By Construction

∠ABC=∠BDC→→[Each being 90°]

∠ACB=∠DCB→→[Reflexive angles , →Reflexive Property of Congruence]

→→→ΔABC~ΔB DC→ [AA criterion for similarity]

When, triangles are similar,corresponding angles are equal and corresponding sides are proportional.

BC²=AC×DC            -------------------(1)

In ΔADB and ΔB AC

B D ⊥ AC→→By Construction

∠ABC=∠ADB→→[Each being 90°]

∠DAB=∠CAB→→[Reflexive angles , →Reflexive Property of Congruence]

→→→ΔADB~ΔB AC→ [AA criterion for similarity]

When, triangles are similar,corresponding angles are equal and corresponding sides are proportional.

 AB²=AC × AD     -------------------(2)

Adding (1) and (2), we get

AB²+BC²=AC × AD +AC × CD

AB²+BC²=AC ×(AD +CD)

AB²+BC²=AC × AC

AB²+BC²=AC²

Hence proved.

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