Quick question for Geometry

Nachosaurus · Poincare Conjecture Offline Joined: 02 Jun 2009 Posts: 243

are all consecutive interior angles supplementary? no matter if lines parallel or not?

**Posted:** Thu Oct 22, 2009 7:44 pm

_________________
http://www.artofproblemsolving.com/Forum/weblog.php?w=1711

Light up your life Idea

AndrewTom

Hi. Unless I've misunderstood your question, the answer is that they are only supplementary when the lines are parallel.

**Posted:** Thu Oct 22, 2009 10:41 pm

fishythefish

To add to what AndrewTom said, no, they're not supplementary unless the lines are parallel.

Many of those kinds of theorems, like the Corresponding Angle or the Alternate Exterior Angles, are only true if the lines intersected by the transversal are parallel.

For an example in your particular case, extend the sides of a polygon, like a regular hexagon. The sum of any two (consecutive or not) interior angles is 240 degrees.

**Posted:** Fri Oct 23, 2009 12:51 pm

_________________
I am NOBODY. NOBODY is PERFECT. Therefore, I am PERFECT. Ninja

There are 3 types of people in the world. Those who can count and those who can't. maybe

ATTENTION ALL CALCOHOLICS!!! Know your limits. Don't drink and derive. Rotfl

PowerOfPi

The lines must be parallel. On the other hand, if you have supplementary consecutive interior angles, then the lines must be parallel.

**Posted:** Fri Oct 23, 2009 1:00 pm

_________________
Sign up for MOCK AMC!

fishythefish

Yes, you can use the converse to prove that the lines are parallel.

**Posted:** Fri Oct 23, 2009 1:08 pm

_________________
I am NOBODY. NOBODY is PERFECT. Therefore, I am PERFECT. Ninja

There are 3 types of people in the world. Those who can count and those who can't. maybe

ATTENTION ALL CALCOHOLICS!!! Know your limits. Don't drink and derive. Rotfl

O M G

They are only supplementary if the interior angles are made by parrallel lines.

**Posted:** Sat Oct 24, 2009 7:34 pm

cgyao15

Don't post the SAME answer OVER AND OVER again.

**Posted:** Sun Oct 25, 2009 5:21 am

_________________
Check out my new avatar made by Izzy. PM her to get one!