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 xx 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 = ____