2.3f:Quadrilaterals M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving polygons GSE’s - Trapezoids CCSS:

Trapezoids Base Base- the parallel sides legLeg – nonparallel sides A Quadrilateral with exactly 1 pair of parallel sides Base angles- angles formed by the base and a leg 2 different pairs of base angles in each trapezoid

Th. 6-16: The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases. Draw the median The median is the segment that joins the midpoints of the legs

Given the trapezoid, find x. Example of a median

Example Find x

Example (2,3) (0,3) (4,-1) (-1,-1) 1) Find the coordinates of the endpoints of the median EF 2) Find the length of AB, CD, and EF E (-.5, 1) F (3,1)

Example 1) Find the coordinates of the endpoints of the median AB 2) Find the length of AB, NL, and MP

Isosceles Trapezoid A Trapezoid where the legs are CONGRUENT

Theorem 6-14: Both pairs of base angles in an isosceles trapezoid are congruent AB C D List the angles that are Congruent by this theorem:

Example A R T E Isosceles Trapezoid TEAR Find the measure of each angle in the trapezoid ANS: 89 91

Th. 6.15: The diagonals of an isosceles trapezoid are congruent A Q U R This theorem tells us: Do they bisect each other?

EXAMPLE Determine if the figure can be classified most specifically as a parallelogram, rectangle, or trapezoid.

Properties