Section 6 6 Notes Trapezoids EQ What are

Section 6. 6 Notes: Trapezoids EQ: What are some properties of trapezoids and kites?

Vocab! Quadrilateral with exactly 1 pair of parallel sides Trapezoid A Bases (parallel sides) Base B Base angles are ∠A & ∠B, ∠C & ∠D Legs (nonparallel sides) Leg Base Angles (base and 1 leg) D C Isosceles Trapezoid Base If the legs of a trapezoid are congruent, then it is an isosceles trapezoid

Isosceles Trapezoid Base Angles Theorem Isosceles Trapezoid Base Angles Converse Isosceles Trapezoid Diagonals Theorem If a trapezoid is isosceles, then each pair of base angles is congruent G H F J If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid A trapezoid is isosceles if and only if its diagonals are congruent. Q R T S

Examples of Isosceles Trapezoid Example 1: Each side of the basket shown is an isosceles trapezoid. If m∠JML = 130 , KN = 6. 7 feet, and LN = 3. 6 feet. Find m∠MJK. 130°

You try! • Yes, isosceles trapezoid diagonals theorem Yes, isosceles base angles theorem

How do you prove an isosceles trapezoid with coordinate geometry? - Use slope to compare opposite sides (one pair of opposite sides are parallel) - Use distance formula to compare lengths of legs (isosceles trapezoid if the legs are congruent)

Examples of Coordinate Geometry Example 2: Quadrilateral ABCD has vertices A(5, 1), B(– 3, – 1), C(– 2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.

Vocab! The segment that connects the midpoints of the legs of the trapezoid Mid-segment A B Trapezoid Mid. Segment Theorem F E C D

Example of Mid-segment Example 3: In the figure, is the mid-segment of trapezoid FGJK. What is the value of x?

You Try! WXYZ is an isosceles trapezoid with median. Find XY if JK = 18 and WZ = 25.

Vocab! Kite A quadrilateral with exactly two pairs of consecutive congruent sides Kite Diagonals Theorem B A C D Kite Opposite Angles Theorem If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent K J L M

Example 5 If WXYZ is a kite, find m∠XYZ. 121°

Example 6 If MNPQ is a kite, find NP.

Example 7 If BCDE is a kite, find m∠CDE. 130°

You Try! For trapezoid HJKL, T and S are midpoints of the legs. a. If HJ = 14 and LK = 42, find TS. b. If LK = 19 and TS = 15, find HJ. c. If HJ = 7 and TS = 10, find LK. d. If KL = 17 and JH = 9, find ST.

You Try! EFGH is a quadrilateral with vertices E(1, 3), F(5, 0), G(8, – 5), H(– 4, 4). a. Verify that EFGH is a trapezoid.

You try cont. b. Determine whether EFGH is an isosceles trapezoid. Explain. Test distance of the legs