Trapezoids Chapter 6.6

TrapezoidDef: A Quadrilateral with exactly one pair of parallel sides.  The parallel sides are called the bases.  The non-parallel sides are called the legs.  A trapezoid has two pairs of base angles. If the legs are congruent, then it is called an isosceles trapezoid.

Trapezoid Base Base Angles Leg Isosceles Trapezoid

Isosceles Trapezoid Theorem Isosceles Trapezoid Theorem Isosceles Trapezoid  Each pair of base angles are .

Another Isosceles Trapezoid Theorem Another Isosceles Trapezoid Theorem Isosceles Trapezoid  Its diagonals are .

Midsegment Theorem for Trapezoids Midsegment Theorem for Trapezoids The Median or Midsegment of a trapezoid is // to each base and is one half the sum of the lengths of the bases. (average of the bases) Midsegment = B1 B2 Midsegment

DEFG is an isosceles trapezoid with median (midsegment) MN Find m  1, m  2, m  3, and m  4 if m  1 = 3x + 5 and m  3 = 6x – 5.

WXYZ is an isosceles trapezoid with median (midsegment) Find XY if JK = 18 and WZ = 25.

ABCD is a quadrilateral with vertices A(5, 1), B(–3, 1), C(–2, 3), and D(2, 4). Determine whether ABCD is an isosceles trapezoid. Explain.

Lesson 6 Ex3 Identify Trapezoids slope of Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid.

Lesson 6 Ex3 Identify Trapezoids Answer:Since the legs are not congruent, ABCD is not an isosceles trapezoid. Use the Distance Formula to show that the legs are congruent.

1.A 2.B 3.C Lesson 6 CYP3 A. QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2), S(1, 4), and T(6, 4). Verify that QRST is a trapezoid. A.yes B.no C.cannot be determined

1.A 2.B 3.C Lesson 6 CYP3 B. QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2), S(1, 4), and T(6, 4). Determine whether QRST is an isosceles trapezoid. A.yes B.no C.cannot be determined

Lesson 6 Ex4 Median of a Trapezoid A. DEFG is an isosceles trapezoid with median (midsegment) Find DG if EF = 20 and MN = 30.

Lesson 6 Ex4 B. DEFG is an isosceles trapezoid. Find m  1, m  2, m  3, and m  4 if m  1 = 3x + 5 and m  3 = 6x – 5. Consecutive Int. Angles Thm. Substitution Combine like terms. Divide each side by 9 Answer: If x = 20, then m  1 = 65 and m  3 = 115. Because  1   2 and  3   4, m  2 = 65 and m  4 = 115.

A.A B.B C.C D.D Lesson 6 CYP4 A.XY = 32 B.XY = 25 C.XY = 21.5 D.XY = 11 A. WXYZ is an isosceles trapezoid with median (midsegment) Find XY if JK = 18 and WZ = 25.

A.A B.B C.C D.D Lesson 6 CYP4 A.m  3 = 60 B.m  3 = 34 C.m  3 = 43 D.m  3 = 137 B. WXYZ is an isosceles trapezoid. If m  2 = 43, find m  3.

Homework Chapter 6.6  Pg 359 3,4, 17-22