3 Proofs

A

abc123

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Oct 23, 2008
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Hi, These are the only problems left of the eight. Thanks for the previous help

3.Given: Segment FL is congruent to Segment AK; Segment SF is congruent to segment SK
M is the midpoint of SF; N is the midpt. Of SK
Prove: AM congruent to LN


4.Given: <1 is congruent to <2; angle 3 congruent to angle 4; angle 5 congruent to angle 6
Prove: BC congruent to ED



7.Given: Point K lies inside triangle ABC
Prove: measure of angle k is greater than measure of angle C
 
Re: 8 problems.

I didn't see a edit button so i had to post again. I forgot to say that for problem one i came up with this info also: Angle EDH = 45 angle EHD=45 Ang. HDG = 45 angle DHG=4 all angles in that square are right angles as well
 
Re: 8 problems.

There's an edit button at the upper right top of your post.
 
Re: 8 problems.

You made a "10 problems" post in Oct/08:
viewtopic.php?f=10&t=31089&p=119885#p119885

You were told we don't do homework here, and to read "Read before posting".

Nobody here is interested (except Mark!) in typing pages of stuff...

I suggest you post your current 8 problems one by one (a post for each)
PLUS show your work and where you're stuck.
 


It's nice to have a choice of exercises.

I choose exercise 6.

To show that ABCD is a parallelogram, we show that opposite sides are parallel because that's the definition of a parallelogram.

Use the slope formula to calculate the slope of the line passing through points A and B.

Use the slope formula to calculate the slope of the line passing through points C and D.

Since the slopes turn out to be the same, you've shown that side AB is parallel to side CD because two lines with the same slope are parallel.

Do the same thing to show that side AD is parallel to side BC.

For the second question in exercise 6, use the slope formula to find the slopes of the two diagonals (AC and BD). By showing that these two numbers are negative reciprocals, you show that the diagonals are perpendicular, right?

For the last question in this exercise, I'll give you a hint.

Use the distance formula to determine all four side lengths. What do you discover?

PLEASE, show your work (or explain what you're thinking, if you get stuck), if you need more help with exercise 6.

 
Re: 8 problems.

Ok, the problems i most need help with are 7, 3 and 4. The reason i didn't real post much of what i was thinking is because i had already taken so much time to type up the problems and make the drawings i was pretty bored. Sorry.

Thanks mmm for the help with number 6 :D

Number 7 i really have no idea how to do. They look like it is possible to be CPCTC (corresponding parts of congruent triangles are congruent) but its obvious the triangles aren't. No transversals for corresponding angles, and no vertical angles. Help please

Number 3 could be proved by proving the triangles FAM and KLN congruent. I know FM = NK so that is 1 side, but not sure about how to get the other info to prove the triangles congruent.

For number 4 CA = CD because the two base angles are congruent so it has to be isosceles and angle 1 already = angle 2 so only one more side is needed Maybe it has something to do with G or F because why mark them otherwise

Number 1 i looked up that each angle in a regular hexagon is = to 120 degrees. I think i need to find a way to prove triangles DEF and HEF congruent so i can say that angle EFD = angle EFH and angle EFD is 60 i think. not sure if i'm heading in the right direction or not

Number 8 i dont really no what to do i just know it is less than 6 feet. IS there some formula i need to use to solve this?
 
Re: 8 problems.

I didn't ask for anyone to do the whole problem... In the beggining of my post i said i wasn't sure where to start on a lot of them.
 
Re: 8 problems.

abc123 said:
Hi, these are 8 hard problems i have to solve. I could use help on where to start on some of them, and others where to go next. Info given in the pictures is black, info i marked is red.

1.1.ABCDEF is a regular hexagon and EDGH is a square. Find the measures of <EFH, <FHD and <DFH.

more info that i found is in the second post.


2.Draw an isosceles triangle and join the midpoints of its sides form another triangle. What can you deduce about this second triangle? Explain


3.Given: Segment FL is congruent to Segment AK; Segment SF is congruent to segment SK
M is the midpoint of SF; N is the midpt. Of SK
Prove: AM congruent to LN


4.Given: <1 is congruent to <2; angle 3 congruent to angle 4; angle 5 congruent to angle 6
Prove: BC congruent to ED


5.The coordinates of three vertices of a parallelogram are A (-1,0), B (2,-2) C(2,2). Find all possibilities for the coordinates of the fourth vertex. Be sure to include an explanation for each possibility you provide.


6.You are given the points A(-4,1) B(2,3) and C(4,9) and D(-2,7). Show that ABCD is a parallelogram with the perpendicular diagonals. What special name is given to ABCD? Explain.


7.Given: Point K lies inside triangle ABC
Prove: measure of angle k is greater than measure of angle C


8.Two vertical poles have heights of 6 feet and 12 feet. A rope is stretched from the top of each pole to the bottom of the other. How far above the ground do the ropes cross? (hint: the lengths of y and z do not affect the answer.)
Click to expand...


Ok...I was GOING to try to help you with problem 7...which says "point K lies inside triangle ABC....etc."

Looking at your diagram, I don't see any point K....would you care to tell us what the problem REALLY says? And, would you also show us what you have done to try to solve the problem?

When we can see your work on a problem, we will have a better idea of how to help you.
 
Re: 8 problems.

abc123 said:
Hi, these are 8 hard problems i have to solve. I could use help on where to start on some of them, and others where to go next. Info given in the pictures is black, info i marked is red.
Click to expand...

"where to go next" implies that you have already DONE some work.

I see NO work on any of these problems.

For instance, in problem 1 you are given that ABCDEF is a REGULAR hexagon...doesn't that tell you something? (If not, please review the definition of a regular polygon.)

Then...take ONE PROBLEM at a time, and show us your work. I'll try to help you if I see some of your work!

If you can't be bothered to do that (because it is boring???), then you are on your own.
 
Re: 8 problems.

Number 7 i really have no idea how to do. They look like it is possible to be CPCTC (corresponding parts of congruent triangles are congruent) but its obvious the triangles aren't. No transversals for corresponding angles, and no vertical angles. Help please

Number 3 could be proved by proving the triangles FAM and KLN congruent. I know FM = NK so that is 1 side, but not sure about how to get the other info to prove the triangles congruent.

For number 4 CA = CD because the two base angles are congruent so it has to be isosceles and angle 1 already = angle 2 so only one more side is needed Maybe it has something to do with G or F because why mark them otherwise

Number 1 I think the anlge measures I'm looking for are EFH = 15 DFH = 45 FDH = 75; would appreciate confirmation though.

Number 8 i dont really no what to do i just know it is less than 6 feet. IS there some formula i need to use to solve this?


I guess you guys didn't see the post right above that one. Those are my thoughts so far on the ones that i am having trouble with. currently number 6, 2 and 5 are solved. also point X is point K I did a typo making it.
 
Re: 8 problems.

At first i was wondering what you were doing posting here at midnight, but then i realized you lived across the country :lol:

Here is my work for number 1:
DEH = 90
DEF = 120
DEH + DEF + FEH = 360
210 + FEH = 360
FEH = 150
EF = ED (parts of same regular shape)
EF = EH
Triangle EFH is Isosceles so EFH = EHF
150 + 2 measure of EFH = 180
2 m EFH = 30
EFH = 15
EHD = 45, FHE = 15 15+45 = 60 FHD = 60
AFE = 120, AFD=90, so DFE = 30
DFH = 30 + 15 = 45


For number 7
1. -------- 1. Given
2. m angle C = 180 - (A+B); m Angle K = 180 - (A+B) 2. Anlges in a triangle add up to 180
3. Angle CBA + Angle CAB > Angle XBA + Angle XAB 3. Whole is greater than the part
4. stuck on what to say next


For number 3
1.------- 1. Given
2. AL = AL 2. Reflexive POE
3. Al + FL = AK + FL 3. Segment addition postulate
4. FA = LK 4. Subtraction POE
5. FM = NK 5. Defn. midpt (???)
6. what included angle are you talking about?

For number 4.
1.------- 1. Given
2. CG = FD 2. Base angles are congruent; Isosceles triangle (is there something else i should say)
3. angle 7 + angle G = 180, angle 8 + angle F = 180 3. definition of supplementary angles
4. Angle 7 + angle G = Angle 8 + angle F 4. Angle addition postulate (???)
5. Angle G = Angle F 5. Substitution(??) or subtraction POE
I dont really understand what your doing with angles BGA and EFA
 
3.Given: Segment FL is congruent to Segment AK; Segment SF is congruent to segment SK
M is the midpoint of SF; N is the midpt. Of SK
Prove: AM congruent to LN

For number 3
1.------- 1. Given
2. AL = AL 2. Reflexive POE
3. Al + FL = AK + FL 3. Segment addition postulate
4. FA = LK 4. Subtraction POE
5. FM = NK 5. Defn. midpt (???)
6. what included angle are you talking about?
Click to expand...

Note: before step 5, you should insert the Given that SF and SK are congruent.

Angles F and angle K are congruent: angles opposite the congruent sides of an isosceles triangle are congruent.
 
well, thanks for all the help. I'm pretty much done working on these now as I've made my final decisions and its due tomorrow.
 
abc123 said:
well, thanks for all the help. I'm pretty much done working on these now as I've made my final decisions and its due tomorrow.
Click to expand...
You've "decided" ? :shock:
Did Pythagoras "decide" that a^2 + b^2 = c^2 ?
 
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