1. G4.3: The Midsegment Theorems
Goal Using Midsegments of Triangles and Trapezoids.
Goal Using Properties of Midsegments.

2. Concept: 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 as long.

3. Concept: Identifying Parallel Segments
What are the three pairs of parallel segments in triangle DEF?
RS || ____
ST || ____
TR || ____

4. Concept: Similar Triangles
The midsegment of a triangle creates 2 similar triangles
∆XYZ ~ ∆UVZ
LYXZ = LVUZ so
mLVUZ = 65º
Find the mLVUZ. X
65O U Z Y V

5. Concept: Using Midsegments of a Triangle
a) In ∆XYZ, which segment is parallel to
b) Find YZ and XY

6. Concept: Using Midsegments of a Triangle cont.
In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU.
5 ft
16 ft
TU = ________
PR = ________

7. Concept: Using Midsegments of a Triangle cont.
In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY.
14 cm
53 cm
ZY = ________
MN = ________

8. Example 6
In the diagram, ED and DF are midsegments of triangle ABC. Find the value of x and DF. 52
3x- 4
x = ________ 10
DF = ________ 26

9. You Try!
Given: DE = x + 2; BC =
Find the value of x and DE.
x + 2

10. Concept: Trapezoid definition
A Trapezoid is a quadrilateral with only one pair of parallel sides.

11. Concept: Isosceles Trapezoid
Isosceles Trapezoids have congruent legs.
In a Isosceles Trapezoid each pair of base angles are congruent.

12. Concept: Definition of a Trapezoid Midsegment
Midsegment connect the midpoints of the legs.
EF is the midsegment of trapezoid ABCD

13. Concept: Trapezoid Midsegment Formula
The Midsegment is equalto half the
sum of the parallal sides.

14. Concept: Trapezoid Midsegment Formula
Example: Find NO
The Midsegment equal half the parallel sides sum.

15. Example: Find the value of x.
Concept: Trapezoid Midsegment Formula
Example: Find the value of x.
The Midsegment equal half the parallel sides sum.
x = 3