1. Theorems Involving Parallel Lines and Triangles
Keystone Geometry:
Using Theorems, Midpoints, and Triangles

2. Theorem:
If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every
transversal. If
and AC = CE , then BD = DF.

3. Theorem:
A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
If M is the midpoint of
XY and , then N is the midpoint of XZ.

4. The Midsegment
The segment that joins the midpoints of two sides of a triangle is called the Midsegment.
The Midsegment:
Is parallel to the third side.
Is half as long as the
third side.
If M is the midpoint of XY and N is the midpoint of XZ, then MN || YZ and MN = 1/2 YZ.

5. are parallel, with AB = BC = CD.
If QR = 3x and RS = x+12,
then x=____
If PQ = 3x - 9 and QR = 2x - 2,
If QR = 20, then QS=____
If PQ = 6, then PR=____ and PS=____
If PS = 21, then RS=____
If PR = 7x - 2 and RS = 3x + 4, then x=____
If PR = x + 8 and QS = 3x - 2, then x=____ A P 6 Q B C R 7 D S 40 12 18 7 10 5

6. Example: M is the midpoint of XY and N is the midpoint of XZ.
If MN = 6, then YZ =_____.
If YZ = 20, then MN =_____.
If MN = x and YZ = 3x - 25,
Then x =_____, MN = _____,
And YZ =_____.
If <XMN = 40, then
<XYZ =_____. 12 10 25 25 50 40
They are
Corresponding
Angles.