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Math Help - Similar Triangle

  1. #1
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    Similar Triangle

    Given two similar triangles ABC and DEF, determine the measurement of the unknown sides.
    AB = 8cm
    DF = 10cm
    A = D = 60°
    AC = 12cm
    EF = 9cm



    How should I draw a triangle of ABC and DEF from these values ? If AB and DF, how can I get ABC ? And what unknown sides ? Im confused :S


    Another question I have:

    2 sides of one triangle are in proportion to 2 sides of a second triangle. One angle - not the contained angle - is equal to another angle - not the contained angle - in the second triangle.

    Is this a similar triangle ? If not why.
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  2. #2
    Senior Member mollymcf2009's Avatar
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    There are several ways to deal with this depending on what subject this is for. Is this for a trig class?
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  3. #3
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    Grade 10 Math, the whole unit is named "similar triangles" the next unit will be trigonometry.
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  4. #4
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    Have you covered the law of cosines yet?
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  5. #5
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    Not in this Unit. Unknown values were solved by doing something with the corresponding sides. We also covered solving proportions.
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  6. #6
    Senior Member mollymcf2009's Avatar
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    Given two similar triangles ABC and DEF, determine the measurement of the unknown sides.
    AB = 8cm
    DF = 10cm
    A = D = 60°
    AC = 12cm
    EF = 9cm

    You are drawing 2 separate triangles. Triangle ABC & Triangle DEF

    I assume you have used the pathagorean theorum? a^2 + b^2 = c^2

    Draw two triangles that are similar. Similar triangles have the exact same angle measurements on all three angles, but they can have different lengths of sides.
    On your triangles, mark the three corners ABC on one and DEF on the other, make sure that you A on the first is in the same place as D on the other, since their angles are both 60 degrees. Then mark your other corners and write the measurements of the sides that are given. Once you have your triangles labeled, use the pathagorean theorum to solve for your unknown sides. Remember that c^2 is always your hypotenuse!! Hope that helps! Good luck!
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  7. #7
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    I have marked the triangles,and I also have A and D on the same place in 2 similar triangles with the same degree. On Triangle 1 I have:
    A-B=8
    A-C=12
    B-C= ?

    using aČ+bČ=c2
    I get 64+144=208 --> sqr(208)= 14.4
    So, is 14.4 correkt for B-C ?

    I did the same thing on Triangle # 2.
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  8. #8
    Senior Member mollymcf2009's Avatar
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    I have marked the triangles,and I also have A and D on the same place in 2 similar triangles with the same degree. On Triangle 1 I have:
    A-B=8
    A-C=12
    B-C= ?

    using aČ+bČ=c2
    I get 64+144=208 --> sqr(208)= 14.4
    So, is 14.4 correkt for B-C ?

    Right idea, but you need to subtract! 144 - 64 = 80
    Attached a picture so you can see what all this looks like. It is kinda hard to explain without a picture!

    \sqrt{80} * I would just leave it as a square root. The answer as a decimal is really messy and long.

    a^2 and b^2 are the two legs of the triangle and c^ is your hypotenuse. You are trying to find the measurement of the other leg of the triangle.
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  9. #9
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    Similar Triangles

    Hello
    Quote Originally Posted by Serialkisser View Post
    Given two similar triangles ABC and DEF, determine the measurement of the unknown sides.
    AB = 8cm
    DF = 10cm
    A = D = 60°
    AC = 12cm
    EF = 9cm



    How should I draw a triangle of ABC and DEF from these values ? If AB and DF, how can I get ABC ? And what unknown sides ? Im confused :S
    I'm sorry, but this question can't be correct. The information given is contradictory.

    See the attached diagram.

    Bear in mind that you can only use Pythagoras' Theorem when you know that the triangle is right-angled - and you don't know this here.

    You could now find the length of the side BC using the Cosine Rule: a^2 = b^2 + c^2 -2bc\cos A. Then find another angle using the Sine Rule, and the third angle using angle sum = 180 degrees.

    Looking at the triangle DEF, you can find the angle E using the Sine Rule, and hence the other angle and sides.

    But, given those measurements, the triangles are not then similar - the angles of one triangle have to be the same as the angles of the other for them to be similar, and the sides in the same ratio.

    Quote Originally Posted by Serialkisser View Post
    Another question I have:

    2 sides of one triangle are in proportion to 2 sides of a second triangle. One angle - not the contained angle - is equal to another angle - not the contained angle - in the second triangle.

    Is this a similar triangle ? If not why.
    No, the equal angles must be opposite to the corresponding sides, and you cannot be certain that this is so.

    For example, if the triangles are ABC and DEF, and we know that the side BC corresponds to side DF, and AC corresponds to DE - in other words the ratios are equal, BC : DF = AC : DE - then the angles opposite these pairs of corresponding sides must be equal: A = E and B = F. And you cannot be sure that this is so from the information given.

    Grandad
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  10. #10
    Senior Member mollymcf2009's Avatar
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    They haven't learned any trig functions in this class yet, so I didn't see any other way to go about it. It does seem that there is info missing. I saw that 60 degrees and figured that maybe it was just a 30, 60, 90 triangle.. Did you change any part of that question? Is it worded exactly as it is in your homework?
    Last edited by mollymcf2009; January 24th 2009 at 12:05 AM.
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  11. #11
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    Thats exactly how it is in my homework.

    Thanks for the answeres :-)
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