Geometry Lesson 6 6 Trapezoids and Kites Objective

Geometry Lesson 6 – 6 Trapezoids and Kites Objective: Apply properties of trapezoids. Apply properties of kites.

Trapezoid What is a trapezoid? A quadrilateral with exactly one pair of parallel sides. Bases – the parallel sides l Legs – the nonparallel sides l Base angles – the angles formed by the base and one of the legs l Isosceles trapezoid l congruent legs

Theorem 6. 21 l If a trapezoid is isosceles, then each pair of base angles is congruent.

Theorem 6. 22 l If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid.

Theorem 6. 23 l A trapezoid is isosceles if and only if its diagonals are congruent.

The speaker shown is an isosceles trapezoid. If m FJH = 85, FK = 8 in. and JG = 19 in. Find each measure. 19 95 KH FH = JG FH = 19 FK + KH = 19 8 in 85 8 + KH = 19 KH = 11 95 85

WXYZ is Isosceles trap. 10 cm 15 cm 45 135 XZ 25 cm XV 10 cm 45

Quadrilateral ABCD has vertices A (-3, 4) B (2, 5) C (3, 3) and D (-1, 0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. To be a trapezoid the quad must have one set of parallel sides. Slope of AD = -2 Slope of BC = -2 The figure is a trapezoid (AB and DC obviously not parallel) To be isosceles the diagonals must be congruent. Trapezoid ABCD is not an isosceles trapezoid.

Quadrilateral QRST has vertices Q(8, -4) R(0, 8) S(6, 8) T (-6, -10). Determine whether it is an isosceles trapezoid. Slope of QR = 3/2 Slope of TS = 3/2 Slope of RS = 0 Slope of QT = 3/7 Since one pair of parallel sides QRST is a trapezoid. Trapezoid QRST is not an isosceles trapezoid.

Midsegment of a Trapezoid Midsegment of a trapezoid l The segment that connects the midpoints of the legs of the trapezoid.

Theorem Trapezoid Midsegment Theorem l The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.

In the figure segment LH is the midsegment of trapezoid FGJK. What is the value of x? (2) 30 = x + 18. 2 11. 8 = x

Trapezoid ABCD is shown below. If FG II AD, what is the x-coordinate of point G? G is the midpoint of segment DC. The x-coordinate is 10. 5

Kite A quadrilateral with exactly two pairs of consecutive congruent sides.

Theorem 6. 25 l Theorem If a quadrilateral is a kite, then its diagonals are perpendicular. Where else have learned about the diagonals being perpendicular? l Square & Rhombus Why does this work for all 3 figures? l Is a Square and a Rhombus considered a Kite? l

Theorem 6. 26 l If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

If FGHJ is a kite, find the measure of angle GFJ Kites have exactly one pair of opposite congruent angles 2 x + 128 + 72 = 360 2 x + 200 = 360 2 x = 160 x = 80 x x

If WXYZ is a kite, find ZY. (PZ)2 + (PY)2 = (ZY)2 82 + 242 = (ZY)2 640 = (ZY)2 Remember to simplify!

x 38 2 x + 38 + 50 = 360 2 x + 88 = 360 2 x = 272 x = 136 50 x

If BT = 5 and TC = 8, find CD. 5 8 (BT)2 + (TC)2 = (BC)2 52 + 82 = (BC)2 89 = (BC)2 BC = CD

Homework Pg. 440 1 – 7 all, 8 – 24 EOE, 36 – 48 EOE, 66, 70 – 76 E, 82