Smile 發問時間: 科學及數學數學 · 1 個月前

Maths problem: how to do, thanks?

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2 個解答

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  • 匿名使用者
    1 個月前
    最佳解答

    Question:

    In the figure, ABC is a triangle and D, P and E lie on BC. It is given that AP = 8 cm, BD = EC = 9 cm and ∠ABC = ∠ACB.

    (a) Show that ΔABE ≅ ΔACD.

    (b) It is given that DP = EP = 6 cm.

    (i) Show that ΔACP is a right-angled triangle.

    (ii) Hence find AC.

    (c) Is  ΔACD a right-angled triangle? Explain your answer.

    https://s.yimg.com/tr/i/c176320ffce34dc0b800358aa9...

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    Solution:

    (a)

    In ΔABE and ΔACD,

    BE = BD + DE

          = CE + DE ...... ( given )

          = CD

    ∠ABE =  ∠ACD ...... ( given )

    AB = AC ...... ( sides opp. eq. ∠s )

    ∴ ΔABE ≅ ΔACD ...... ( SAS )

    (bi)

    In ΔABP and ΔACP,

    AB = AC ...... ( proved )

    BP = BD + DP

          = CE + EP ...... ( given )

          = CP

    AP = AP ...... ( common side )

    ∴ ΔABE ≅ ΔACD ...... ( SSS )

    ∴ ∠APB = ∠APC  ...... ( corr. ∠s, ≅ Δs )

    ∠APC = (∠APB + ∠APC)/2 = 180°/2 = 90° ...... ( adj. ∠s on st. li. )

    ∴ ΔACP is a right-angled triangle.

    (bii)

    AC

    = √(AP² + CP²) ...... ( Pyth. theorem )

    = √[8² + (9 + 6)²]

    = 17 

    (c)

    AC² + AD²

    = AC² + AP² + DP² ...... ( Pyth. theorem )

    = 17² + 8² + 6²

    = 389

    ≠ (9 + 6 + 6)² = CD²

    ∴ ΔACD is not a right-angled triangle.

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    https://yahoo.uservoice.com/forums/924010-yahoo-an...

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  • 1 個月前

    謝謝你,原來要利用畢氏定理才計算得到.我想了很久也想不通.現在終於明白了

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