Class of Feb. 5, 2009

Today as usual we check over our homework which was on page 358 and # 13-18 all and 21-25 all. Once we check all of our homework, Ms. Saatkamp began explaining # 24 and 25 which were difficult and many people had some trouble with them.

In number 24, we are told that we have to find EC, GC, and EF. While we knows that ED//AB, AB= 10, BC= 6, AC= 8, CD= 5 and GE= 3.

Now lets just focus on finding EC and GC first. In the angels of triangles ABC and CEG you can notice that angle FBC is congruent to angle LCD since they are both on // lines that are cut by a transversal and the pair of angels are alternate interior. Also the other pair of angels is angel AFG and angel GEC which like the top are alternate interior which means that they are congruent. Therefore, now that we have at least two angles we know that by AA Similarity (Postulate 7-1) triangle ABC ~ triangle CEG. Therefore all we have to do now is match the proportional sides like this:

Then we know the numbers that the sides are equal to, therefore just replace the variables with the numbers and for CE and CG just replace them with variables:

Afterwards all you have to do is just cross multiple the variable-proportional with the non- variable proportional and just repeat that but with the other variable-proportional in order to get the answers. If you did the algebra correct then x= 5 and y=4; so just replace the variables x with CE and y with CG. Now lets move on to EF, if you had notice that AFCD is a parallelogram then you might remember that besides the sides are // the sides are also congruent there since we know that CD =5, that means that EF=5.

Finally we are done with #24, lets move to the next one #25. As you may be looking at the book because of the diagram, we know that we have to find AE, AC, CF, CB, CD and EF. Also it tells us that:

EF//AB, AD= 9, DB= 16 and EC= 2(AE)

Now lets see the sides, since that EF//AB and that there is a transversal which is AC that cuts through them, therefore that means that angle CEH is congruent to EAD because they are corresponding angles. Also, the same goes for angle CFH which is congruent to FBD since they are also corresponding angels but the tranvesal is CB. Now that we have two pairs of congruent angles, that means that triangle ABC ~triangle ACD by AA Similarity (Postulate 7-1). Therefore we all do is just match the proportional sides like this:

And then we just replace them with numbers but lets ignore the middle one and focus on the other two:

Then all we have to do is simple algebra add, multiplied, and also you have to do the square root but the answer is x=5. Therefore we know that AE= 5 and AC= 15. Now in order to solve the other one we must find out what BC is therefore since we know that that triangle ACD is a right triangle and the two legs AC and AD then we can use the Pythagorean Theorem and squaring the number and finding the square root, we finally know that CD= 12. Therefore we can input that and cross multiplied and now we know that BC= 20.

So far we have most of them solved expect for CF and EF. Maybe you have noticed before but triangle ABC is congruent to triangle EFC by AA Similarity. They are congruent because angle CEH is congruent to angle CAD since they are corresponding angles. Also the same thing applies for angle CFH and angle CBD. Now we just have to match the proportional sides with their matches like this:

Then after we just replace them with numbers and begin working on solving them.

So just cross multiply one with one that has a variable and the other one that doesn't and then just repeat this expect with the other variable-proportional. Afterwards EF = 16.7 (I rounded it) and FC=13.333... Now we finally have all the answers and that's means with are done with number 25!!

But before you stop reading this post just remember to study for the Quiz tomorrow and Ms. Saatkamp had gave our a sheet to practice which is good or just review the HW, and DON'T FORGET TO BRING A CALCULATOR, because you can use it during the quiz just that you cant bring a ipod, itouch, cell phone to calculate.