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Determine if AB is parallel to CD?

I had this question on a test but my teacher is saying that it's not parallel, however I am fairly certain that it is parallel. Angle ABD and BDC are both equal making them alternate interior angles therefore making BD a transversal. However she is basing it off angles ADB and CBD claiming they aren't equal. Well of course they aren't equal because they are not within the range of the two lines that are trying to be proved parallel.

Attachment 26820

Re: Determine if AB is parallel to CD?

Quote:

Originally Posted by

**pacoMac** I had this question on a test but my teacher is saying that it's not parallel, however I am fairly certain that it is parallel. Angle ABD and BDC are both equal making them alternate interior angles therefore making BD a transversal. However she is basing it off angles ADB and CBD claiming they aren't equal. Well of course they aren't equal because they are not within the range of the two lines that are trying to be proved parallel.

Attachment 26820

The sum of the interior angles of a triangle is 180 degrees. Use triangle BCD and that will give you x. Then use the sum if interior angles for triangle BAD. That should give you a good start.

-Dan

Re: Determine if AB is parallel to CD?

Yes I already got that which I didn't input into the previous post, and x was 25. Making CDB = 44 degrees and angle ABD = 44 since 180 - 93 + 43 = 44. And that is where I assumed that AB and DC were parallel but my teacher is convinced that it isn't.

Re: Determine if AB is parallel to CD?

Quote:

Originally Posted by

**pacoMac** Yes I already got that which I didn't input into the previous post, and x was 25. Making CDB = 44 degrees and angle ABD = 44 since 180 - 93 + 43 = 44. And that is where I assumed that AB and DC were parallel but my teacher is convinced that it isn't.

The two are parallel if and only if $\displaystyle m\left( {\angle A} \right) + m\left( {\angle D} \right) = 180^o $.

I agree that are parallel.