Transcript Chapter 5.1 Midsegments of Triangles

Chapter 5.1 Midsegments of
Triangles
Vocabularies
Midsegment =a segment connecting the midpoints of two
sides.
 In the figure D is the midpoint of AB and E is the midpoint of AC
.
 So,DE is a midsegment.
Theorem 5.1 Triangle Midsegment
Theorem
 If a segment joins the midpoints of two sides of a triangle,
then the segment is parallel to the third side, and is half its
length
 If AD = DB and AE = EC,
 Then
DE // BC
and
DE 
1
2
BC
Example #1
 Find the value of x.
 Here P is the midpoint of AB, and Q is the midpoint of BC. So, PQ is a
midsegment.
 Therefore by the Triangle Midsegment Theorem,
PQ 
1
BC
2
 Substitute.
x
1
6
2
x3
 The value of x is 3.
Vocabularies
 Coordinate proof = You proof by using the coordinate. You
begin the proof by placing a triangle in a convenient spot on
the coordinate plan. You then choose the variables for the
coordinates of the vertices
Example #2
 In
 HJ=
 JK=
 FG=
EFG, H, J, and K are midpoints. Find HJ, JK, and FG.
Example #3
 In
DEF, A, B, and C are midpoints. Name pairs of parallel
segments.
 Midsegments?
 Parallel segments?
**Hint: There are 3 midsegments, so there should be 3 pairs of
parallel segments
Classwork/Homework
 Take out a piece of paper
 Pgs 262-263 #2-32evens, 33