6.5 Trapezoids & Kites

Trapezoid Is a quadrilateral with exactly 1 pair of parallel sides

Trapezoid A B C D leg BASE

If the legs are congruent then the trapezoid is an isosceles trapezoid.

Theorem 6.14 If a trapezoid is isosceles, then each pair of base angles is congruent.

Theorem 6.15 If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Theorem 6.16 A trapezoid is isosceles if and only if its diagonals are congruent.

Midsegment The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

THM 6.17 The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of its bases

EX 1 Find the length of MN. 13 PQPQ M N S R 10 16

EX 2 Find the value of x x

A Kite A quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent.

Theorem 6.18 If a quadrilateral is a kite, then its diagonals are perpendicular.

Theorem 6.19 If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

Ex 3 Find the measure of the sides. Round to the nearest tenth. LM = 3.6 LO = 3.6 ON= 5 MN = 5 L M N O

Ex 4 Find the m  L. 110  40  100  L M N O

Ex 5 Find the m  L. 35  55  135  xx L M N O

Add Trapezoid and Kite to your foldable.

Goal: Identify midsegments and use properties of midsegments of a triangle

Midsegment – a segment that connects the midpoints of two sides of a triangle.

Midsegment Theorem A B C XY AC || XY XY = ½ AC The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

Ex 1: UW and VW are midsegments of  RST. Find UW and RT. R S T V W U 12 8 UW = 6 RT = 16

Ex 2: X, Y, and Z are the midpoints of  UVW. Complete each statement. U X V W Z Y a.If VW = 6a, then XY = ___ b. m  WZY = 2b + 1, then m  WVU = ______. c. XZ  _______. d. If YZ = c, then UV = ____