HL Postulate

HL Postulate

If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent (Figure 6 ). 

Figure 6 The hypotenuse and one leg (HL) of the first right triangle are congruent to the corresponding parts of the second right triangle.

It is important that the HL Postulate ONLY applies to RIGHT triangles. So when using in a proof, one statement must be that the triangles are right triangles.


Thanks to everyone for their support in getting me to do the blog.
Joey

Types of Triangles

SCALENE TRIANGLE- NO SIDES ARE CONGRUENT

EQUILATERAL TRIANGLE-ALL THREE SIDES CONGRUENT

 

 

EQUILATERAL IF AND ONLY IF EQUIANGULAR

ISOSCELES TRIANGLE-

• AT LEAST TWO SIDES CONGRUENT
• THE TWO CONGRUENT SIDES ARE CALLED THE LEGS
• THE NON-CONGRUENT SIDE IS CALLED THE BASE
• (AN EQUILATERAL TRIANGLE IS STILL AN ISOSCELES TRIANGLE)

YOU'RE WELCOME

3.4: Beyond CPCTC

Today in class, we learned about 4 new terms about triangles and their proofs.

These terms are Perpendicular Bisector, Angle Bisector, Altitude, and Median


Perpendicular Bisector- a straight line that is perpendicular to a segment at its midpoint

Angle Bisector- a straight line that divides an angle into 2 equal parts

Altitude- a straight line through a vertex of the triangle and perpendicular to the oppposite side

Median- a straight line from a vertex of a triangle to the midpoint of the oppsite side

Ok thats pretty much everything we learned about in class today. In section 3.4, we will be doing the same thing as 3.3 but going a bit further by using the statement that two triangles are congruent. A few of these terms will also show up in the homework.

Thanks,

Robbie

3.3 CPCTC and Circles

Today in class we learned about circles and CPCTC, or Corresponding Parts of Congruent Triangles are Congruent. 

First of all, we defined what a circle is. A circle is a set of points that are equidistant from a given point. Also, the circle is just the circumference, or the outside border, and the inside is called the "disk", as shown below:

Secondly, every circle is named by its center point. Again, the circle consists of only the "rim", as the book refers to it, so the center point is not part of the circle. To show the name of the circle, you would draw a small circle with a dot in the middle and then write the letter of the center. (Sorry I couldn't find a good picture of the circle symbol)

Lastly, we learned how to use CPCTC in a proof and that radii imply congruent segments. 

This was basically what we did, except it was obviously one circle, circle O. I couldn't figure out a good way to make the proof (sorry), but we proved that seg. AB was congruent to seg. CD, with CPCTC reason they were congruent. 

That's pretty much what we did in class today!

-Jessica 

Section 3.2 : Three ways to prove triangles congruent

Today we learned how to prove congruent triangles using postulates and theorems. We proves the postulates and theorems using a triangle construction worksheet. You know the postulate or theorem works when there is only one true possible way to make the triangle complete. (sorry it's blurry, but this is the worksheet we did during class)

I put check marks next to the postulates/theorems that worked, and an x by the one that did not. S means Side, and A means angle.
Postulates/theorems that will work:
SSS
SAS
ASA
AAS
Postulates/theorems that will NOT work:
SSA
AAA

*Working postulates/theorems may be used in a proof as a justification to prove justification, and you only have to right the side-angle combination. (i.e. SAS, SSS,...ect.)

Triangles may also be similar, meaning there angles are congruent but sides are not. (Hence the reason AAA does not work)

Well I'm pretty sure that's about all we covered :D
Yupp!
Have fun with the homework, sorry this is so late!
-Maggie Ridenour

Chapter 2 Review

I created a wiki for our review sheet.

Every problem is on a different page.  You can upload an idea, the beginning of a solution, or a whole solution.  You can also edit anybody else's response to improve it.

Here's our wiki:
http://hga1f10.wikispaces.com/

If you've never used a wiki, check out this video.
http://www.youtube.com/watch?v=-dnL00TdmLY

Section 2.8 Vertical Angles

Today in class we learned about vertical angles. Vertical angles are formed when two lines intersect and are opposite from each other. Two angles are vertical angles i the rays forming the sides of one angle and the rays forming the sides of the other angle are opposite rays, or rays that are collinear and have a common endpoint. You can conclude this in the following proof:(sorry if it is a little hard to read.)

That's what we learned in class today. Sorry it took so long to post this. I had a tennis match until seven and didn't get home until 7:30.

Jacob

P. S. The post time is wrong, I posted this around 8:45.