1. Triangles and Parallel LinesTriangles and Parallel Lines
You will learn to use proportions to determine whether lines
are parallel to sides of triangles.
Nothing New!
2. Triangles and Parallel LinesTriangles and Parallel Lines
You know that if a line is parallel to one side of a triangle and intersects the
other two sides, then it separates the sides into segments of proportional
lengths (Theorem 9-5).
The converse of this theorem is also true.
Theorem 9-6
If a line intersects two sides of a triangle and separates the
sides into corresponding segments of proportional lengths,
then the line is parallel to the third side.
ED
CB
A
9
6
6
4
then,If
9
6
6
4
= DEBC ||
3. Triangles and Parallel LinesTriangles and Parallel Lines
Theorem 9-7
If a segment joins the midpoints of two sides of a triangle, then
it is parallel to the third side, and its measure equals
________ the measure of the third side.one-half
ED
CB
A
and,ofmidpointtheisDIf AB
2x
x
then,ofmidpointtheisE AC
and,|| BCDE BCDE
2
1
=
4. Triangles and Parallel LinesTriangles and Parallel Lines
ED
CB
A
and,ofmidpointtheisDIf AB
22
11
then,ofmidpointtheisE AC
and,|| BCDE BCDE
2
1
=
5
5
8
8
x
( )x 22
2
1
=
x 11=
Use theorem 9 – 7 to find the length of segment DE.
5. Triangles and Parallel LinesTriangles and Parallel Lines
A, B, and C are midpoints of the sides of ΔMNP.
Complete each statement.
C
BA
N P
M
2) If BC = 14, then MN = ____
1) MP || ____AC
28
3) If mMNP = s, then mBCP = ___s
4) If MP = 18x, then AC = __9x
6. Triangles and Parallel LinesTriangles and Parallel Lines
A, B, and C are midpoints of the sides of ΔDEF.
2) Find the perimeter of ΔABC
1) Find DE, EF, and FD. 14; 10; 16
20
4) Find the ratio of the perimeter of
ΔABC to the perimeter of ΔDEF.
20:40 =
C
BA
D F
E
8
753) Find the perimeter of ΔDEF 40
1:2
7. Triangles and Parallel LinesTriangles and Parallel Lines
A
D
C
B
ABCD is a quadrilateral.
E is the midpoint of AD
F is the midpoint of DC
H is the midpoint of CB
G is the midpoint of BA
Q1) What can you say about EF and GH ?
E
G
H
F
(Hint: Draw diagonal AC .)
They are parallel
Q2) What kind of figure is EFHG ? Parallelogram
