# Thread: Parallel lines and congruent segments question

1. ## Parallel lines and congruent segments question

Let's take quadrilateral, ABCD, where the following is given:

AC is parallel to BD
AB is perpendicular to BD
AB is congruent to CD

Given the above, is it correct to conclude that CD is also perpendicular to BD, since AB and CD are congruent.

Screen Shot 2017-11-05 at 12.20.23 AM.jpg

2. Originally Posted by kanakku
Let's take quadrilateral, ABCD, where the following is given:

AC is parallel to BD
AB is perpendicular to BD
AB is congruent to CD

Given the above, is it correct to conclude that CD is also perpendicular to BD, since AB and CD are congruent.

Screen Shot 2017-11-05 at 12.20.23 AM.jpg

Yes

But can you support your conclusion with geometric argument (with reference to well known theorems).

3. Thanks for the confirmation. I guess that's where I have been struggling to connect the dots. Which theorems should be used.

4. Where would I start on how to prove that conclusion ?

5. Originally Posted by kanakku
Where would I start on how to prove that conclusion ?
Different geometry courses get to different theorems (or rules) in different orders. What results have you learned recently?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

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