Monday, August 17, 2009

Heavenly Angles

Did you know all the angles in a triangle add up to 180 degrees?

Daisy didn't know this either, so I set out to show her.

First you need a triangle. Mark each of the angles so you will know WHICH of them belong to your triangle. The marks are the curvy little lines in each corner (and I should have marked them with one, two and three lines respectively to show that they are different measures. But I didn't)

Did you see the straight lines in the first picture. Well cut off each corner of your triangle on the straight lines.


Now, like a puzzle, fit the 3 corners from your triangle together (you might need to click on the picture to blow it up so you can see this better). All the corners should point the same way and touch. Keep an eye on the angles you marked earlier.

Do you notice what happens? When the three corners are fit together, they form a straight line. Every time! (We tried out 3 different triangles to check this) Guess how many degrees are in a straight line? Yup. 180. Therefore, the three corners of a triangle add up to 180.

How is this useful? Well, if you know the measures of two of the angles, you can find the measure of the third. Ta Da!

It also comes in handy when finding the measures of angles in other shapes such as rectangles, parallelograms (I love to spell that word!) and when working with angles and parallel lines.

Did I mention that I got 100% on every test in high school geometry and finished the class with an A+?

Anyone have any proofs I can work out???????

5 comments:

Jimmie said...

Ooohhh... I love this! Proving or showing or discovering the rule is so much more meaningful than memorizing a rule. Thanks for contributing to the CM carnival.

I will bookmark this as well for future reference.

prayingmother said...

This is an awesome post. So simple and so obvious, but I sure never thought of it. I'm going to remember this one.

Thanks

sarah in the woods said...

Very nice demonstration!

{ jamie } said...

Wonderful!

Keri said...

Good stuff for a visual learner.