Presentation on theme: "Trapezoids and Kites 1/16/13 Mrs. B. Objectives: Use properties of trapezoids. Use properties of kites."— Presentation transcript:
Trapezoids and Kites 1/16/13 Mrs. B
Objectives: Use properties of trapezoids. Use properties of kites.
Using properties of trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides called bases. A trapezoid has two pairs of base angles. Ex. D and C And A and B. The nonparallel sides are the legs of the trapezoid.
Using properties of trapezoids If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.
Isosceles Trapezoid If a trapezoid is isosceles, then each pair of base angles is congruent. A B, C D
Isosceles Trapezoid If a trapezoid is isosceles, then adjacent angles (not bases) are supplementary.
Ex. 1: Using properties of Isosceles Trapezoids Given, angle X is 50 Find
Isosceles Trapezoid A trapezoid is isosceles if and only if its diagonals are congruent. ABCD is isosceles if and only if AC BD.
Midsegment of a trapezoid The midsegment of a trapezoid is the segment that connects the midpoints of its legs.
Theorem 6.17: Midsegment of a trapezoid The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases. MN AD, MNBC MN = ½ (AD + BC)
Ex. 3: Finding Midsegment lengths of trapezoids 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?
Ex. 3: Finding Midsegment lengths of trapezoids Use the midsegment theorem for trapezoids. DG = ½(EF + CH)= ½ (8 + 20) = 14 C D E D G F
Using properties of kites A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Kite theorems Theorem 6.18 If a quadrilateral is a kite, then its diagonals are perpendicular. AC BD
Kite theorems Theorem 6.19 If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent. A C B not = D
Ex. 4: Using the diagonals of a kite WXYZ is a kite so the diagonals are perpendicular. You can use the Pythagorean Theorem to find the side lengths. WX = XY =
Ex. 5: Angles of a kite Find m G and m J in the diagram. 132 ° 60 °