# Thread: 8 Problems ned help with

1. ## 8 Problems ned help with

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.

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

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.

2. Hello, abc123!

2. Draw an isosceles triangle and join the midpoints of its sides form another triangle.
Code:
                A
*
/ \
/   \
/     \
F * - - - * E
/ \     / \
/   \   /   \
/     \ /     \
B * - - - * - - - * C
D
Theorem: The line joining the midpoints of two sides of a triangle
. . . . . . . .is parallel to and one-half the length of the third side.

Hence: . $\begin{array}{ccccc}
FE = \frac{1}{2}BC, & FE \parallel BC \\ \\[-4mm]
ED = \frac{1}{2}AB, & ED \parallel AB \\ \\[-4mm]
FD = \frac{1}{2}AC, & FD \parallel AC \end{array}$

Therefore: . $\Delta D{E}F \sim \Delta ABC$

. . and: . $(\text{area }\Delta D{E}F) \:=\:\tfrac{1}{4}(\text{area }\Delta ABC)$

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.
There are three possible locations for vertex $D.$
Code:
            |       C
|       o
|    *     *
| *           *
*|                *  D
- - o - | - - - - - - - - - o - -
A  *|                * (5,0)
| *           *
|    *     *
|       o
|       B
|
Code:
            |       C
|       o
|    *  *
| *     *
A  *|       *
- - o - + - - - * - -
*   |       *
*   |       *
*   |       *
*   |       o
*   |    *  B
*   | *
*  *|
D o   |
(-1,-4)|
Code:
        D
(-1,4)o   |
*  *|
*   | *
*   |    *  C
*   |       o
*   |       *
*   |       *
*   |       *
- - o - + - - - * - - -
A  *|       *
| *     *
|    *  *
|       o
|       B
|

3. Hey what does the ~ mean? is that like 1/2 of the other triangle or something?

4. Originally Posted by abc123
Hey what does the ~ mean? is that like 1/2 of the other triangle or something?
It would have been good manners to first say something like "Hey, thanks for the help" before demanding to know the definition of a symbol you're expected to recognise: Congruence

I'm closing this thread because I just can't be bothered spending the time making new threads for all your other questions. Please do not post so many questions in one thread - no more than 2 when the images are this big. Otherwise the thread becomes convoluted and impossible to follow.

I'm keeping questions 2 and 5 in this thread but deleting the rest. Please re-post the others and keep in mind what I've said. Thankyou.