Hey gente!!

Today our class was complicated and required us to pay attention.. most of it was Miss Saatkamp explaining the theories, so here it goes: Theorem 7-4 a.k.a Triangle Proportionality Theorem. In the book it says: "If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths. Ok, thats a lot of info, so first lets look at the given. So part one, if a line is parallel to one side of a triangle, in the diagram at the right DE is parallel to BC. Part two of the given, and intersects the other two sides in two distinct point, in the diagram those points are D and E an the two other sides are BA and AC. Know you have the if we need the then. it says, then it separates these sides into segments of proportional lengths. What that means is AD/DB = AE/EC (AD over DB = AE over EC).

possible ERROR!! miss saatkamp enphasized a lot the fact that many students assume that if AD/DB = AE/EC then it also equals DE/DB... THAT IS WRONG.

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Theorem 7-5

Theorem 7-5 states that "If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side. OK, this one is the converse of the one above. If: DE intersects AB and AC, and AD/DB= AE/EC, Then DE//BC

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Theorem 7-6

I know the diagram seems different, but its bassically the same diagram sideways, just so we understand that it isnt always necessary in the other direction! This theorem says that "A segment (note that it is segment instead of line) whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle and its length is one-half the length of the third side". Again there is a lot of info, so lets go by parts. Given: DE intersects AB and AC at their midpoint (E is AC's midpoint and D is BC's midpoint). (Dont forget that because oit is a midpoint the segments in between are congruent). THEN: DE//BC and DE=1/2 BC

This theorem is based on similar triangles.

ex. The example miss saatkamp gave in class was that if AC=10, DC=2, AB=12 and AE=6 what can you say DE//BC?

The answer is no! because AE=6 it is the midpoint, something that does not happen on side AC.

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Corallary 7-1

This corallary states that "If three or more parallel lines intersect two transversals, then they cut of the transversals propotionally" Using the diagram, if l//m//n... p and q are transversals ... then AB/BC=DE/EF. There are other proportional comparisons you can make, just be careful NOT to cross compare (INCORRECT EXAMPLE of cross comparison- DE/BC=AB/EC).

Corallary 7-2

if: l//m//n and AB is congruent to BC

then: any other transversal is cut into congruent segments. I know some people in class were confused about def. of transversal. The Definition is: a line that intersects two or more lines in a plane at different points.

Homewor is page 366 and 367 #12-29 all except for 26.. there is also SS to read, biology to complete worksheet and english reading and the paragraph...btw dont forget to sign the ecoclub thingy...

beijos and good luck!