Warm up: Identify the best name for the given traits of each quadrilateral. 1.) ABCD has two sets of parallel sides and a right angle. 2.) HGDT has 2 sets of opposite congruent sides and the left side is congruent to the top 3.) YHBG has 2 sets of opposite congruent angles and its diagonals are perpendicular.

6.5 TRAPEZOIDS AND KITES LEQ: What are the special properties of trapezoids and kites?

Using properties of trapezoids Theorem 6-15  If a trapezoid is isosceles, then each pair of base angles is congruent.   A ≅  B,  C ≅  D AB CD

Proof of part of thm Prove that m<C=m<D A B CD Construct BE so that it’s parallel to AC 2.) AC=BE2.) Opposite sides of parallelograms are congruent 3.) Transitive Property/substitution3.) BE=BD E 4.) m<D=m<14.) Isosceles Triangle Thm. 5.) m<1=m<C5.) Corresponding Angles 6.) m<C=m<D6.) Transitive/Substitution 1 1.) AC=BD, AB//CD1.) Given

Ex. 1: Using properties of Isosceles Trapezoids  PQRS is an isosceles trapezoid. Find m  S, m  Q, m  R and QR. 50 ° PQ SR 2.6

 LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be? (the top of the middle layer must be exactly halfway between the top of the first and 3 rd layers)

Recall midsegment of a triangle  Half the distance of the base

Theorem 6-18: Midsegment of a trapezoid  Different!! The median of a trapezoid is the segment that connects the midpoints of its legs. Thm 6-18 says the median:  Is parallel to each base: MN ║ AD, MN ║ BC  Has a length equal to the average of the base lengths MN = ½ (AD + BC)

Example: Both are medians Find the value of x.  Find the value of x x x + 3

Theorem 6-16 The diagonals of an isosceles trapezoid are congruent. Why??*Bonus* proof due Monday Ex: Find the value of x if AC = 2x + 10 and BD = 3x + 4 AB D C

Kites Recap: What are the requirements in order to be a kite? *note*: one pair of opp. <‘s is bisected (the diag. that splits the congruent legs) Theorem 6-17: The diagonals of a kite are _____________. What other quadrilaterals share this characteristic?

Example: Find the measures of the numbered angles. 32˚ 46˚

What rules can we derive for kites? 1.) diagonals are perpendicular 2.)adjacent sides congruent, but not all sides congruent