- #1
Taylorrr8394
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Given : line AD is congruent to line BE
Prove: line AE is congruent to line BD
please help! i have no idea what to doo!
Prove: line AE is congruent to line BD
please help! i have no idea what to doo!
Proving Congruence of Line AE and BD
- Thread starter Taylorrr8394
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In summary, the conversation is about the definition of congruent lines and whether a line segment can be considered congruent to a line. There is some disagreement about the definition and usage of congruence, with one person suggesting that "congruent" means the same length while another suggests it also includes the same direction and placement. The concept of a line segment as a finite part of a line is also discussed.
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tiny-tim
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Welcome to PF!
Hi Taylorrr8394! Welcome to PF!
But that obviously isn't true
Have you left something out?
What are A B D and E (and whatever happened to poor little C?
)
Hi Taylorrr8394! Welcome to PF!
Taylorrr8394 said:
But that obviously isn't true
Have you left something out?
What are A B D and E (and whatever happened to poor little C?
)- #3
jth01
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Why isn't it?
If line AD is congruent to line BE, doesn't that mean they are the same line, so then any two pair of lines made of those letters (line AB, line AD, line AE, line BD, line BE, line DE) are also describing the same line and thus congruent? Am I missing something?
If line AD is congruent to line BE, doesn't that mean they are the same line, so then any two pair of lines made of those letters (line AB, line AD, line AE, line BD, line BE, line DE) are also describing the same line and thus congruent? Am I missing something?
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tiny-tim
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jth01 said:
Hi jth01!
Perhaps your book is using a different definition of "congruent".
The definition I was taught is that two lines are congruent if they are the same length … but they can be at any place, and in any direction.
- #5
jth01
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Doesn't a line have infinite length?
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tiny-tim
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line segment
Hi jth01!
hmm … interesting point!
I agree that "a line", on it own, must be infinite, and a finite part of a line is "a line segment".
But if particular points are specified, to name the line, then standard usage is that "the line through A and B" is infinite,
but "the line AB" is the line segment.
jth01 said:
Hi jth01!
hmm … interesting point!
I agree that "a line", on it own, must be infinite, and a finite part of a line is "a line segment".
But if particular points are specified, to name the line, then standard usage is that "the line through A and B" is infinite,
but "the line AB" is the line segment.
1. What is the definition of congruence in geometry?
Congruence in geometry refers to the condition in which two geometric figures have the same shape and size. In other words, the figures are identical and can be superimposed on top of each other. This is typically proven by showing that all corresponding angles and sides are equal.
2. Why is it important to prove congruence between two lines?
Proving congruence between two lines is important because it allows us to confidently say that the two lines are exactly the same. This means that they have the same length, angles, and other properties. It also helps to establish relationships between different parts of a geometric figure, which can be useful in solving problems and making accurate constructions.
3. What are the methods for proving congruence of two lines?
There are several methods for proving congruence of two lines, including SAS (side-angle-side), SSS (side-side-side), ASA (angle-side-angle), AAS (angle-angle-side), and HL (hypotenuse-leg). These methods involve comparing corresponding angles and sides of the two lines to determine if they are equal, and using this information to conclude that the lines are congruent.
4. What is the difference between congruence and similarity?
While congruence refers to the exact same shape and size of two lines, similarity refers to the same shape but different sizes. In other words, similar figures have proportional sides and angles, but not necessarily equal ones. Proving congruence requires showing that all corresponding parts are equal, while proving similarity only requires showing that the ratios of corresponding parts are equal.
5. Can two lines be congruent if they are not identical?
No, two lines cannot be congruent if they are not identical. Congruence requires that all corresponding angles and sides are equal, which means the lines must have the same shape and size. If the lines are not identical, they may be similar, but they cannot be congruent.
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