Hello, abc123!
2. Draw an isosceles triangle and join the midpoints of its sides form another triangle.
What can you deduce about this second triangle? Explain Code:
A
*
/ \
/ \
/ \
F *    * E
/ \ / \
/ \ / \
/ \ / \
B *    *    * C
D
Theorem: The line joining the midpoints of two sides of a triangle
. . . . . . . .is parallel to and onehalf the length of the third side.
Hence: .$\displaystyle \begin{array}{ccccc}
FE = \frac{1}{2}BC, & FE \parallel BC \\ \\[4mm]
ED = \frac{1}{2}AB, & ED \parallel AB \\ \\[4mm]
FD = \frac{1}{2}AC, & FD \parallel AC \end{array}$
Therefore: .$\displaystyle \Delta D{E}F \sim \Delta ABC$
. . and: .$\displaystyle (\text{area }\Delta D{E}F) \:=\:\tfrac{1}{4}(\text{area }\Delta ABC)$
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 $\displaystyle D.$ 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
