Geometry 6.5 Trapezoids and Kites

Goals Know definitions of trapezoid and kite. Use properties of them to solve problems. December 8, 2018 6.5 Trapezoids and Kites

Quadrilaterals Quadrilaterals Parallelograms Rhombuses Rectangles Some quadrilaterals are parallelograms. Parallelograms Rhombuses Rectangles Squares December 8, 2018 6.5 Trapezoids and Kites

But not all… Some quadrilaterals are Trapezoids. And some quadrilaterals are Kites. Quadrilaterals Parallelograms Kites Rhombuses Rectangles Trapezoids Squares December 8, 2018 6.5 Trapezoids and Kites

Trapezoid A quadrilateral with exactly one pair of parallel sides. December 8, 2018 6.5 Trapezoids and Kites

Trapezoid The parallel sides are the BASES. The non-parallel sides are the LEGS. December 8, 2018 6.5 Trapezoids and Kites

These are trapezoids: December 8, 2018 6.5 Trapezoids and Kites

Isosceles Trapezoid The legs are congruent. December 8, 2018 6.5 Trapezoids and Kites

Isosceles Trapezoid Theorems 6.14 Each pair of base angles is congruent. December 8, 2018 6.5 Trapezoids and Kites

Isosceles Trapezoid Theorems 6.15 If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. December 8, 2018 6.5 Trapezoids and Kites

Isosceles Trapezoid Theorems 6.16 A trapezoid is isosceles if and only if its diagonals are congruent. B C A D December 8, 2018 6.5 Trapezoids and Kites

Problem Find the measure of 1, 2, and 3 if the figure is an isosceles trapezoid. 75 1 3 2 December 8, 2018 6.5 Trapezoids and Kites

Solution In an isosceles trapezoid, base angles are congruent. 1 is _______. 75 75 75 1 3 2 December 8, 2018 6.5 Trapezoids and Kites

The bases are parallel, so 3 = _____. 105 75 75 105 3 2 December 8, 2018 6.5 Trapezoids and Kites

Again, since base angles are equal, 2 = ______. 105 75 75 105 105 2 December 8, 2018 6.5 Trapezoids and Kites

Your Turn CDEF is an isosceles trapezoid with CE = 10 and E = 95. Find DF, C, D and F. E ? 95 95 85 ? 85 ? December 8, 2018 6.5 Trapezoids and Kites

Name the vertices of CDEF. C must be where? Now label the rest. CE is a diagonal and is 10. DF = ____. (In an isosc. trap., diags are .) 10 E D 95 95 85 85 F C December 8, 2018 6.5 Trapezoids and Kites

Triangle Review The midsegment of a triangle connects the midpoints of two sides. The midsegment is parallel to the third side and one-half its length. December 8, 2018 6.5 Trapezoids and Kites

Trapezoid Midsegment Connects the midpoints of the legs. December 8, 2018 6.5 Trapezoids and Kites

Midsegment Theorem The midsegment of a trapezoid is parallel to each base and its length is one-half the sum of the bases. A B C D E F December 8, 2018 6.5 Trapezoids and Kites

Example AB = 24 and DC = 30. Find EF. 24 B A E F D C 30 December 8, 2018 6.5 Trapezoids and Kites

Your Turn ? AB = 10 and EF = 15. Find CD. 10 B A 15 E F D C December 8, 2018 6.5 Trapezoids and Kites

Solution ? 20 10 B A 15 E F D C December 8, 2018 6.5 Trapezoids and Kites

Trapezoid Summary A trapezoid has 2 parallel sides. A trapezoid is NOT a parallelogram. The legs of an isosceles trapezoid are congruent. The base angles of an isosceles trapezoid are congruent. The midsegment of a trapezoid is one-half the sum of the two bases. December 8, 2018 6.5 Trapezoids and Kites

Kites A kite is a quadrilateral with two pairs of congruent sides, but opposite sides are not congruent. (They’re not parallel, either.) These are congruent consecutive sides. And these are congruent consecutive sides. December 8, 2018 6.5 Trapezoids and Kites

Kites A kite is a quadrilateral with two pairs of congruent sides, but opposite sides are not parallel. There are NO parallel sides. December 8, 2018 6.5 Trapezoids and Kites

Kite Properties The diagonals of a Kite are perpendicular. (Theorem 6.18) One pair of opposite angles is congruent. (Theorem 6.19) December 8, 2018 6.5 Trapezoids and Kites

Problem GHJK is a kite. Find GH. H J G 5 2 K December 8, 2018 6.5 Trapezoids and Kites

Solution 52 + 22 = GK2 29= GK2 Use Pythagorean Theorem. H J G 5 2 K Segments GK and GH are congruent. H J G 5 2 K December 8, 2018 6.5 Trapezoids and Kites

Another Kite Problem RSTU is a kite. Find R, S, T. S x + 30 R T x 125 U December 8, 2018 6.5 Trapezoids and Kites

Solution ? 40 70 The sum of the angles in a quadrilateral is 360. 125 R x + 30 T 40 x 70 125 U The sum of the angles in a quadrilateral is 360. x + 30 + 125 + x + 125 = 360 2x + 280 = 360 2x = 80 x = 40 December 8, 2018 6.5 Trapezoids and Kites

Questions? December 8, 2018 6.5 Trapezoids and Kites

True or False? In ABCD, diagonals AC and BD are perpendicular. ABCD is a kite. True or False? FALSE. Why? The diagonals of a rhombus are also perpendicular. December 8, 2018 6.5 Trapezoids and Kites