6.5 Trapezoids A D B C A Trapezoid - a quadrilateral with: *one pair of parallel sides (called bases) *two pairs of base angles *one pair of nonparallel sides (called legs) If legs are congruent – isosceles trapezoid A D B C

Ex 1: Given Trapezoid ABCD with , identify the segments or angles as bases, consecutive sides, legs, diagonals, base angles, or opposite angles. A D B C c) consecutive sides d) diagonals opposite angles a) bases e) b) legs f) base angles

Thm 6.14 – If a trapezoid is isosceles, then each pair of base angles is congruent. Thm 6.15 – If a trapezoid has a pair of congruent base angles, then it is isosceles. B C A D

Thm 6.16 – A trapezoid is isosceles iff its diagonals are congruent. B C A D If , then Trapezoid ABCD is isosceles.

Ex 2: Given isosceles trapezoid PQRS, find and . 50° P Q The trapezoid is isosceles, so base angles are congruent (the measures are equal). are consecutive, hence supplementary.

Ex 2: Given isosceles trapezoid PQRS, find and . 50° P Q Again, base angles in an isosceles trap are congruent!

Proceed with the PowerPoint when finished. Recall, the midsegment of a triangle joins the midpoints of the sides. For a trapezoid, it joins the midpoints of the trapezoid’s legs. midsegment Click on the link. Read up to the formula to determine the length of a trapezoid’s midsegment: http://www.mathopenref.com/trapezoidmedian.html Proceed with the PowerPoint when finished.

Ex 3: Find the length of midsegment . A B M P 20m

C B A F 8 D E 9 x Ex 4: Find x. Multiply both sides by 2 to get rid of the fraction

*ask for your handout on 6.5 once you’ve gotten to this slide Assignment Page 359 #10 – 24 *ask for your handout on 6.5 once you’ve gotten to this slide