Can you answer these math questions?

http://img136.imageshack.us/img136/6083/mathsp4.jp...

If you can, also provide how you got the answer. I need to know these to continue to play NCAA CU football! :-O

1 Answer

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  • 1 decade ago
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    #1:

    Since ABM is isosceles, that means AM = AB

    also in BMN, then BM = BN

    A median cuts the side into two equal halves.

    So...

    AE = EB

    AD = DM

    and since AB = AM, then

    AE = EB = AD = DM

    Same for the other triangle

    BP = PM = BC = CN

    Also, in an isosceles triangle, the medians from the base angles are congruent. So...

    BD = ME

    and

    NP = MC

    So.... Using substitution:

    AE + ME + MC + BC = 32

    AE = AD

    ME = BD

    MC = NP

    and

    BC = BP

    So...

    AD + BD + BP + NP = 32

    **********

    #2:

    ABN is equilateral, which means each of its angles is 60 degrees (and all three sides are equal length).

    AM is a median, which means NM = MB.

    Since NM = MB, AN = AB, and angle ANB = angle ABN = 60 degrees, then

    triangle ANM is congruent to triangle ABM (by the side-angle-side theorem)

    Because they are congruent, then corresponding parts of the triangles are congruent, which means

    angle ANM = angle ABM

    since angle NAB = 60 degrees (definition of equilateral triangle), and NAB = NAM + MAB

    then NAB = MAB = 30 degrees.

    Triangle AME is equilateral (given). So

    angle AME = angle MEA = angle EAM = 60 degrees

    since we know angle MAB = 30 degrees (from above),

    and MAE = MAB + BAE

    then BAE = 30 degrees.

    Since we know AM = AE (equilateral triangle)

    and AC = AC (reflexive property),

    and angle MAC = angle CAE = 30

    by side-angle-side, we again know that

    triangle AMC is congruent to triangle AEC

    Because corresponding parts of triangles are congruent, we know that MC = CE

    Since MC = CE, then AC must be the median of triangle AME.

    **********

    #3:

    We know ABM is equilateral, that means all angles of that triangle are 60 degrees. So, angle AMB is 60 degrees.

    Since BME are collinear (make a straight line), then you can find angle AMC.

    AMC + AMB + CME = 180

    AMC + 60 + 30 = 180

    AMC = 90 degrees.

    You can use trigonometry on triangle ACM (since it's a right triangle) to find AM.

    sin (angle ACM) = (AM) / (AC)

    sin 30 = AM / 36

    1/2 = AM / 36

    18 inches = AM

    Source(s): Sorry, I don't know how to do #4.
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