? 發問於 科學及數學數學 · 1 十年前

急~~~中二MATHS~~~20分

兩條maths題

1). ABCD is a square and E is a point such that CDE is an equilateral triangle.

a). Draw a diagram to represent the given information (two possible cases).

b). Is △ABE an isosceles triangle? Find suitable angles to verify your judgement.

2). A regular n-sided polygin has 5 more sides than a regular m-sided polygon,

and the sum of interior angles of the former is twice that of the latter. Fing the

values of m and n.

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    1 十年前
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    兩條maths題

    1). ABCD is a square and E is a point such that CDE is an equilateral triangle.

    a).

    Draw a diagram to represent the given information (two possible cases).

    i can just tell u about the diagram

    Case1:

    E is a point inside the square

    Case2:

    E is a point outside the square.

    b).

    Is △ABE an isosceles triangle? Find suitable angles to verify your judgement.

    Case1:

    consider △AED and △BEC

    AD = BC(prop of square)

    ED = EC(sides of equilateral triangle)

    angle EDA = angle ECB = 30

    so,△AED and △BEC is a pair of equal triangle(A.S.S)

    so,AE = EB(side corresponding to equal △)

    Case2:

    consider △BCE

    BC = CE (given)

    angle BCE

    = 90 + 60

    = 150

    so,

    angle EBC = 15(base angle at isos triangle)

    angle of ABE

    = 90 - 15

    = 75

    consider △ACE

    AD = DE(given)

    angle of ADE

    = 90 + 60

    = 150

    angle DAE = 15(base angle at isos triangle)

    angle BAE = 75

    = angle ABE

    so,△ABE is an isosceles triangle both in case 1 and 2.

    2).

    A regular n-sided polygin has 5 more sides than a regular m-sided polygon,

    and the sum of interior angles of the former is twice that of the latter. Fing the

    values of m and n.

    n = m + 5-----[1]

    (n - 2) x 180 = 2 x (m - 2) x 180-------[2]

    sub [1] into [2]

    (m + 5 - 2) = 2(m - 2)

    m + 3 = 2m - 4

    m = 7

    n = 12

    資料來源: eason mensa
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