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caarolin9
14.07.2019 •
Mathematics
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)
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Ответ:
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.
Ответ:
C. m4 = 180° - m3