Objectives:Develop and use formulas for the sums of the measures of interior and exterior angles of polygons

3.7 Midsegments of Triangles & Trapezoids

Warm-Up:Seven & eleven are both odd numbers. Your task is to make them both even without performing a mathematical operation.

711

a segment whose endpoints are the midpoints of the two sides

Mid-segment of a Triangle:

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.

Triangle Mid-Segment Conjecture:

In triangle DEF, A, B, and C are midpoints. Name pairs of parallel segments.

Find DE

Find AB

D and E are midpoints.Find the measure of <A.

In Triangle EFG, H, J, and K are midpoints. Find HJ, JK, and FG.

Given DE, DF, and FE are the lengths of mid-segments. Find the perimeter of triangle ABC.

Find DE

Mid-segment of a Trapezoid:

a segment whose endpoints are the midpoints of the non-parallel sides

Trapezoid Mid-Segment Conjecture:

A midsegment of a trapezoid is PARALLEL to the bases of the trapezoid and has a measure equal to the average of the base lengths.

Find NO

Find PQ

Find KL

Find KL

Find DE, FG, & HI

Find AB & CD

Find AB, WO, & CD