Trapezoids Chapter 6 6 Trapezoid Def A Quadrilateral

Trapezoids Chapter 6. 6

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

Trapezoid Base Leg Base Angles Base Isosceles Trapezoid Le g

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

Another Isosceles Trapezoid Theorem Isosceles Trapezoid Its diagonals are .

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 = B 1 Midsegment B 2

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

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

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

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. 2. 3. A B C

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 1. 2. 3. A B C

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

B. DEFG is an isosceles trapezoid. Find m 1, m 2, m 3, and m 4 if m 1 = 3 x + 5 and m 3 = 6 x – 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. WXYZ is an isosceles trapezoid with median (midsegment) Find XY if JK = 18 and WZ = 25. A. XY = 32 B. XY = 25 C. XY = 21. 5 D. XY = 11 A. B. C. D. A B C D

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

Homework Chapter 6. 6 u. Pg 359 3, 4, 17 -22