Help on triangle proof question

In summary, Byron tried to solve the problem using vector addition, but was unable to do so because he did not make use of the fact that D is the midpoint of the line segment BC. He then found a solution using coordinate proofs.
  • #1
byronsakic
17
0
Hello,
Here is the question:
question2.jpg

Here are 2 different ways i tried to approach the question:
In the first way, i tried using pythagoreom theorem by making a right angle, but after i did the question i realized since it did not say it was a right triangle, ic annot assume there is a 90 degrees angle and i cannot use the pythagoras theorem.
part1question2.jpg

Second way i tried using vector addition. However you can see at the end i was stuck.
part2question2.jpg

though i believe vector addition is the way to solve this problem, however we had never done any problems involving the squared of a vector unless it was using the pythagoras theorem,
any suggestions in what i did wrong or what i could do?

Sorry for my messy writing hehe.

thanks
byron
 
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  • #2
Byron,

Try this. Drop a perpendicular from A to the line segment BC. Call its length h and the distance between the intersection point and the midpoint x. Now you can use Pythagoras to solve for x and h from which you can calculate AD.
 
  • #3
I know why you can't do it with vector addition: nowhere in your work did you make use of the fact that D is the midpoint of the line segment BC.

(In fact, you didn't even made use of the fact that D is on the line through B and C!)
 
  • #4
didnt i do it in the first try? but if you drop a perpendicular from A to line segment BC then how would u prove that it is a right angle? but i think i did that in first try..

though i am going to try coordinate proofs right now :D i think that is the solution
 
  • #5
I only looked at your vector addition approach. I agree that ought to be the easiest solution. (unless you're particularly adept with synthetic geometry)
 
  • #6
i got the answer by using coordinate proofs and making LS = RS

thanks for all your help :D
 

1. How do I start solving a triangle proof question?

To start solving a triangle proof question, it is important to carefully read the given information and identify any given lines, angles, or triangles. Then, use the given information to start making logical deductions and constructions to prove the desired statement.

2. What are some common strategies for solving triangle proof questions?

Some common strategies for solving triangle proof questions include using congruent triangles, the Pythagorean theorem, and angle relationships such as vertical angles, corresponding angles, and supplementary angles.

3. How can I organize my work when solving a triangle proof question?

It is important to clearly label and mark all given information and any constructions made during the proof. Using a diagram to visually represent the given information and any deductions can also be helpful in keeping the work organized and easy to follow.

4. What is the difference between a two-column proof and a paragraph proof?

A two-column proof is a more structured and concise way of presenting a proof, with statements written on one side and corresponding reasons on the other side. A paragraph proof, on the other hand, is a more narrative and explanatory way of presenting a proof, with all statements and reasons written in paragraph form.

5. What should I do if I get stuck on a triangle proof question?

If you get stuck on a triangle proof question, it can be helpful to review the given information and try to make new deductions or constructions. You can also try working backwards from the desired statement to see what steps need to be taken to reach it. If you are still stuck, it can be beneficial to seek help from a teacher or classmate.

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