Anyone wanna do homework for me ? :\

Almost the end of the first trimester and i dont know what geometry is .

Link : http://img510.imageshack.us/img510/geopw6.jpg/1/w1275.png



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There is a sticky in this forum for a reason...but give me a few minutes :S

You want the WHOLE worksheet done? I don't have that much time at the moment, but here's a brief explanation of the first few.

1) Reflect the triangle over the y axis - keep the points on the same "height" but basically draw the mirror image. For example, point C (-6,1) because point C' (6, 1). If you fold the paper horizontally, the two triangles should overlap.

2) Reflect the triangle over the x axis - keep the points the same distance from the y-axis, but just shift them down. For example, point C (-6, 1) because point C' (-6, -1). Comprende? They should overlap if you fold the paper over the x-axis.

3) MOVE the triangle 5 units to the right and 6 units down. For example, point C (-6, 1) because point C' (-1, -5).

4) Which variable (x or y) determines the distance horizontally? The answer is x, therefore if you want to move it 5 units to the left, horizontally, you need to decrease the x value by 5. So, (x, y) --> (x-5, y)

5) Since horizontal distance is affected by the x, vertical distance is affected by the y value. Therefore, to move it right 2 you increase x by 2, and to move it up 4 you increase x by 4. So, (x, y) --> (x+2, y+4)

6) To move it down, all you have to do is decrease the y value, right? So what you do is (x, y) --> (x, y-2).

6.5) This is going to be a horizontal reflection.

7) This is going to be a translation, moved 5 units right and down 6.

8) This is going to be a vertical reflection.

9) Well, if you're given the points and the relationship, you can just find the new points. As we know the rule is (x,y) -> (x-2, y+3), and the original points: A (4, 2), B (-3, -4), C(-5, 5), we can just calculate the new points.
A' (2, 5), B' (-5, -1), C' (-7, 8)

10) Okay, since we know that in a triangle, AB + BC > AC, AB + AC > BC, BC + AC > AB (the triangle inequality theorem; the sum of any two sides of a triangle must be greater than the third side - this makes sense, because let's just imagine a straight line. It can be broken up into a "fake triangle" if you take any point on that line and call it B, while calling the endpoints A and B. AB + BC = AC, but if it were any shorter, the segments would not reach the ends - make sense?)

Anyways, we know that in a possible triangle, 9, or x could be the longest side [given sidelengths 4, 9, and x]. So, if x is the biggest side, the outer bound would be: 4 + 9 > x, 13 > x -> x < 13. Therefore, we know that x cannot be bigger than 13. Now, what if 9 is the longest side? Our inequality would be 4 + x > 9, thus x > 5. So, the final possible inequality would be:
5 < x < 13. It cannot be equal to 5 or 13, because otherwise we would just have a line.

11) Angle F must be 57, because the angles of a triangle add up to 180. So, the angles (smallest to largest) must be 33, 57, 90. Now, there is not enough information to find the specific sidelengths, but to order them largest to smallest, we can use this theorem: the longest side is always opposite the largest angle in a triangle.

So, opposite from angle 33 (leg DF) is the smallest, opposite from angle 57 (leg DE) is the next largest, and finally the side opposite from the right angle (leg EF) is the greatest.

12) Well, we know that side with length 3 is across from the 16 degree angle, the side with length 7 is across from the 41 degree angle, and the side with length 9 is across from the 126 angle. I don't really want to draw it, but it's not really that difficult. I might attach a drawing that looks something similar to it later.

13) Can't tell. Picture this: why can't you draw AD or DC in such a way that they intersect line AB/BC much closer to point B? The truth is, you can't - there is no restriction on the length of AB/BC, or the length of AD/DC, therefore, you can't tell.

14) DF < KH. There is a theorem that two triangles are congruent if two sides are congruent, and the angle between them (the included angles) are congruent in each of the triangles. A correlary (sp.?) to this theorem is that if the included angle of one triangle is greater than the included angle of the other triangle, so too is the opposite side. One way of thinking about this is to try exaggerating the diagram. Instead of having it be 100 degrees vs. 110 degrees, try making it 100 degrees vs. 170 degrees - the difference is seen easily, so you can pretty safely conclude that 110 vs 110 will not change much [if you keep the other two sides congruent].

15) AB = BC. Call the point on top of A point D, and the point below E. So, you have that line AD is parallel, and congruent to, line CE. Remember the theorem that alternate interior angles are congruent in parallel lines cut by a transversal? If not, trust me - it exists. If so, then that means that angle <ADB = angle <CEB. With this, you can prove that triangle ABD is congruent to triangle CEB, because you have two sides (AD = CE, DB = BE) are congruent, as are the angles between them (<ADB = < CEB). Since the two triangles are congruent, all the sides must be congruent to corresponding sides of the other triangle. Since AD = CE and DB = BE, the only remaining pair of angles is AB = BC. Another way to verify this is through the theorem that sides opposite congruent angles in congruent triangles are congruent, but this is a bit more confusing

16) Assumption: the opposite of what you are trying to prove; Assume: L || M.
Then: by alternate exterior angles are congruent in parallel lines cut by a transveral; Then: alt. exterior angles are congruent.
But: we are given that the alternate exterior angles 71 and 72 are NOT congruent.
So: there is a contradiction given our assumption, therefore our assumption must be false. L is NOT parallel to (can't draw symbol atm) M.

I hope I helped!!

 

Just some of it , Im doin like the ones i only know :\

I really have a bad geometry teacher and tbh i dont know proofs or anything

 

Meh, I'll just do it all - hopefully, I will have helped. Please re-post this in the HW help sticky (http://sythe.org/showthread.php?t=490925) though, so mods can lock this thread.

 

If the teacher was bad, you should of took notes from book. Always helps me when the teacher's teaching style sucks.

 

thats some hardcore stuff

 

lol i dont even know what that is........ wat grade r u in

 

I thought this way easy but calculus wiped the floor with me lol.