1) Please don't waste the time of volunteers by posting the same questions in multiple locations.
2) Please don't try to get others to do your homework for you.
3) These are still fine problems. Let's see how far you get.
a) The side length of a square ABCD is 4. P and Q are points on the sides AB and BC respectively such that BP = 1 and BQ = 3. Prove that angle PAQ + angle PDQ + angle PCQ = 90 degrees.
b) In a quadrilateral ABCD, there is a point X on the side BC such that XA and XD are the angle bisectors of angle BAD and angle CDA respectively. Prove that if AB = BX, then BC = AB + CD.
For the first problem.
The key is at the corner D of the square ABCD. That corner D is 90 degrees....(like all the 3 other corners A,B,C).
Draw the figure on paper. I don't know how to draw on computers.
tan(<PCB) = 1/4
tan(<CDQ) = 1/4 also.
So, <PCB = <CDQ ----------**
tan(<BAQ) = 3/4
tan(<PDA) = 3/4 also
So, <BAQ = <PDA -----------**
In the figure, <BAQ = <PAQ, and <PCB = <PCQ ---------**
At corner D,
<PDA + <PDQ + <CDQ = 90 degrees.
Substitute <PAQ for <PDA, and substitute <PCQ for <CDQ,
Then, <PAQ + <PDQ + <PCQ = 90 degrees. --------proven.
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The second problem is a little bit difficult. Is that the complete problem? No missing information on the quadrilateral ABCD?
To TKHunny,
I believe that the only reason I even post these questions are because:
1) I have no clue how to do them and require assistance
2) I have found a way that takes ages and pages, and wish to see if others are able to enlighten me on how to solve it via an easier method (not everyone has the leisure and time of managing accounts at different locations like you – I simply post it at different locations so that I may receive different solutions from different thinkers and thus it may help me learn how to improve myself in math)
Do you seriously think I don’t try my best to solve these problems? If I could, I wouldn’t be posting on forums and interrupt people from helping to solve other people’s problems.
Furthermore, let me point out that not everyone is as intelligent as you are in math because of their e.g. oh let’s see very young age perhaps? How on earth can I solve these problems when I hardly know anything about geometry?
To ticbol,
Thanx for your method for solving a. I would have never thought of using trigonometry. My teacher only lightly touched upon the topic. I was fiddling with the angles all afternoon.
For b, unfortunately that's all I was given.
Then you probably are in the wrong class. Rethink your goals with your academic couneselor rather than struggling through impossible information.
Notice how this is evidence that your first statement is entirely incorrect. Obviously, even to you, you do have SOME clue.2) I have found a way that takes ages and pages, and wish to see if others are able to enlighten me on how to solve it via an easier method
This is where you seem not to understand what it is you are doing. You are asking for help from volunteers. They help when they can becasue they want to help. When you ask in multiple locations, you imply that your time and energy are of greater value than the time and energy of volunteers. If you need additional and more varied assistance, you should consider paying for it.(not everyone has the leisure and time of managing accounts at different locations like you – I simply post it at different locations so that I may receive different solutions from different thinkers and thus it may help me learn how to improve myself in math)
How can we KNOW this one way or the other if you show nothing at all?Do you seriously think I don’t try my best to solve these problems?
Very good.If I could, I wouldn’t be posting on forums and interrupt people from helping to solve other people’s problems.
It is of no social value to be smart alecky. It continues to mysitify me why honesty is so often mistaken as effrontery, or directness as arrogance. I cannot name a single volunteer on either website who is volunteering solely for his own aggrandizement. You would do well to sling fewer accusations and concentrate on your mathematical studies.Furthermore, let me point out that not everyone is as intelligent as you are in math because of their e.g. oh let’s see very young age perhaps?
It's called learning. That why you are in this class, to learn it. If it was easy, and you knew it already, why would you be in the class?How on earth can I solve these problems when I hardly know anything about geometry?
Thank you for the opportunity to discuss these matters.
What do you say we get down to some mathematics?