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Math Help - Triangle-related Questions

  1. #1
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    Triangle-related Questions

    I have a few questions that I don't completely understand and those are:

    1. What does congruence mean for triangles? [I didn't think it "meant" anything for triangles other than the fact that they are congruent]

    2. Do two congruent triangles have the same area?

    3. Are all triangles with the same area congruent?

    I find all this confusing even though it's pretty basic.
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  2. #2
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    Quote Originally Posted by ~NeonFire372~ View Post
    I have a few questions that I don't completely understand and those are:

    1. What does congruence mean for triangles? [I didn't think it "meant" anything for triangles other than the fact that they are congruent]

    2. Do two congruent triangles have the same area?

    3. Are all triangles with the same area congruent?

    I find all this confusing even though it's pretty basic.
    Hello,

    #1: Two triangles are congruent if their corresponding sides and angles are equal.

    #2: Yes

    #3: No
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  3. #3
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    Could you explain why for number 2 and 3 a bit more?
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  4. #4
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    Quote Originally Posted by ~NeonFire372~ View Post
    Could you explain why for number 2 and 3 a bit more?
    I've attached a drawing of a lot of triangles which have the same area (btw. why?) but they are not congruent because they differ in the length of corresponding sides and the value of corresponding angles.


    EDIT: Have a look here: Congruent Triangles
    Attached Thumbnails Attached Thumbnails Triangle-related Questions-no_congruence.gif  
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  5. #5
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    So...

    Triangles with the same area are "not congruent because they differ in the length of corresponding sides and the value of corresponding angles" and triangles that are congruent always have the same area because the sides and angles are the same?
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  6. #6
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    Quote Originally Posted by ~NeonFire372~ View Post
    So...

    Triangles with the same area are "not necessarily congruent because they differ in the length of corresponding sides and the value of corresponding angles" and triangles that are congruent always have the same area because the sides and angles are the same?
    Correct!
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  7. #7
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    Thanks.
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