9 5 triangles and parallel lines
8
Triangles and Parallel Lines Triangles and Parallel Lines You will learn to use proportions to determine whether line are parallel to sides of triangles. Nothing New!
-
Upload
gwilson8786 -
Category
Technology
-
view
1.164 -
download
1
Transcript of 9 5 triangles and parallel lines
Triangles and Parallel Lines Triangles and Parallel Lines
You will learn to use proportions to determine whether linesare parallel to sides of triangles.
Nothing New!
Triangles and Parallel Lines Triangles 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 , If9
6
6
4 DEBC ||
Triangles and Parallel Lines Triangles 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 , of midpoint the is D If AB
2x
x
then , of midpoint the is E AC
and ,|| BCDE BCDE2
1
Triangles and Parallel Lines Triangles and Parallel Lines
ED
CB
A
and , of midpoint the is D If AB
22
11
then , of midpoint the is E AC
and ,|| BCDE BCDE2
1
5
5
8
8
x x 222
1
x 11
Use theorem 9 – 7 to find the length of segment DE.
Triangles and Parallel Lines Triangles 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
Triangles and Parallel Lines Triangles 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
Triangles and Parallel Lines Triangles 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
Triangles and Parallel Lines Triangles and Parallel Lines
