G4.3: The Midsegment Theorems Goal 1 Using Midsegments of Triangles and Trapezoids. Goal 2 Using Properties of Midsegments.

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.

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

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

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

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 = ________

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 = ________

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

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

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

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

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

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

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

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