Question 159549: Line AB is congruent to line CD, Line AB is parellel to line CD; prove that triangal ABD id congruent to triangle CDB
Help im so confused on what postulates and theorems i would use to prove this
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! use what you know to be true and work from there.
problem states that AB congruent to CD.
problem also states that AB parallel to CD.
looks like you might have a parallelogram.
draw AB above CD and parallel to it but not directly above it (a little to the left or a little to the right is ok).
connect AC with a line, connect BD with a line, connect AD with a line.
AB and CD are the given lines parallel to each other.
AC and BD are additional lines you created to form at least a quadrilateral.
AD is a diagonal from top left of the quadrilateral to bottom right of the quadrilateral.
look at what you have and see what you can assume.
you can assume that AB is congruent to CD because that is given.
you can assume AD is congruent to AD because anything is equal to itself (reflexive property).
you can assume that angle BAD is congruent to angle CDA because alternate interior angles of two parallel lines are equal.
this is enough to prove that triangles ADC and triangles ABD are congruent to each other by SAS (side angle side).
AB is congruent to CD (given)
AD is congruent to AD (all things are equal to themselves)
angle ADC congruent to angle BAD and is positioned between the other two congruent sides.
i think that's your proof.
1. create AC, BD, and AD by construction (any two points make a line - i'm pretty sure you can assume these are postulates without having to prove them - you don't need to construct AB or CD because they were given)
2. prove diagonal AD is equal to itself (this would be a postulate - you don't have to prove it - it's called the reflexive property)
3. prove angle BAD congruent to angle ADC (alternate interior angles of parallel lines are congruent is a postulate of parallel lines).
4. triangles are congruent by SAS (also a postulate)
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it looks like your proof depends on only postulates which were provided in your textbook.
it does not depend on theorems that were proved earlier.
if it did, you could state these theorems as proof in the same way you state postulates as proof. they should not have to be proven again.
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make sure you know your postulates as they are the building blocks for proving theorems and form the basis for what you can assume.
make sure you know what theorems have been proven before since they are additional building blocks that you can use as you progress through the course.
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