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Toán học - Lớp 9
22/10/2023 11:46:20

Cho hình chữ nhật ABCD có AB=9cm, AD=12cm

cho hình chữ nhật ABCD có AB=9cm, AD=12cm kẻ AH vuông góc với BD tại H
a, Tính BD, AH và số đo góc ABD?
b, kẻ HI vuông góc với AB chứng minh AI.AB=DH.HB
c, đường thẳng AH cắt BC tại M và cắt DC tại N . chứng minh HA^2=HM.HN
(làm tròn kết quả số đo góc đến độ )
 
1 trả lời
Hỏi chi tiết
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Tham khảo câu trả lời từ Trợ lý ảo Lazi
a, Ta có AB = 9cm và AD = 12cm. Vì AH vuông góc với BD nên ta có:

BD^2 = AH^2 + AD^2 (theo định lý Pythagoras)
BD^2 = AH^2 + 12^2
BD^2 = AH^2 + 144

Vì AB = 9cm và AD = 12cm, ta có:

BD^2 = AB^2 + AD^2
BD^2 = 9^2 + 12^2
BD^2 = 81 + 144
BD^2 = 225
BD = √225
BD = 15cm

Vậy BD = 15cm.

Ta có AH vuông góc với BD, nên góc AHB là góc vuông. Vì vậy, góc ABD là góc vuông.

b, Ta có HI vuông góc với AB và AH vuông góc với BD, nên HI song song với BD. Khi đó, ta có:

AI/AH = HB/HD (theo định lý đường thẳng chia đôi)
AI/AH = HB/(BD - HB) (vì BD = BH + HD)
AI/AH = HB/(15 - HB)

Ta cần chứng minh AI.AB = DH.HB, ta có:

AI.AB = (AI/AH).AH.AB
AI.AB = (HB/(15 - HB)).AH.AB
AI.AB = (HB/(15 - HB)).(AH + HB).AB
AI.AB = (HB/(15 - HB)).(AH.AB + HB.AB)
AI.AB = (HB/(15 - HB)).(DH.HB + HB.AB) (vì AH.AB = DH.HB)
AI.AB = (HB/(15 - HB)).(DH.HB + HB.(AB - AH))
AI.AB = (HB/(15 - HB)).(DH.HB + HB.AB - HB.AH)
AI.AB = (HB/(15 - HB)).(DH.HB + HB.AB - HB.(BD - HD))
AI.AB = (HB/(15 - HB)).(DH.HB + HB.AB - HB.BD + HB.HD)
AI.AB = (HB/(15 - HB)).(HB.HD + HB.HB - HB.BD + DH.HB + HB.AB)
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD) + DH.HB + HB.AB)
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD) + HB.(DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))

Vì góc ABD là góc vuông, nên góc AHB là góc vuông. Khi đó, góc AHB = 90 độ. Vậy:

AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB))
AI.AB = (HB/(15 - HB)).(HB.(HD + HB - BD + DH + AB
2
0
Vinh
22/10/2023 11:52:07
+5đ tặng

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